{"id":28714,"date":"2023-09-12T14:35:08","date_gmt":"2023-09-12T07:35:08","guid":{"rendered":"https:\/\/ungdung.hotronghiencuu.com\/open\/giao-diem-la-gi"},"modified":"2023-09-12T14:35:08","modified_gmt":"2023-09-12T07:35:08","slug":"giao-diem-la-gi","status":"publish","type":"post","link":"https:\/\/ungdung.hotronghiencuu.com\/open\/giao-diem-la-gi","title":{"rendered":"Giao \u0111i\u1ec3m: \u0110\u1ecbnh ngh\u0129a, thu\u1eadt ng\u1eef v\u00e0 t\u00ednh ch\u1ea5t"},"content":{"rendered":"<p>Giao \u0111i\u1ec3m l\u00e0 \u0111i\u1ec3m h\u1ee3p nh\u1ea5t c\u1ee7a hai ho\u1eb7c nhi\u1ec1u \u0111\u01b0\u1eddng, tuy\u1ebfn \u0111\u01b0\u1eddng ho\u1eb7c \u00fd ki\u1ebfn kh\u00e1c nhau. N\u00f3 l\u00e0 n\u01a1i c\u00e1c y\u1ebfu t\u1ed1 kh\u00e1c nhau g\u1eb7p nhau v\u00e0 t\u01b0\u01a1ng t\u00e1c v\u1edbi nhau \u0111\u1ec3 t\u1ea1o ra s\u1ef1 ph\u00e1t tri\u1ec3n v\u00e0 ti\u1ebfn b\u1ed9. Giao \u0111i\u1ec3m c\u00f3 vai tr\u00f2 quan tr\u1ecdng trong vi\u1ec7c k\u1ebft n\u1ed1i v\u00e0 giao l\u01b0u gi\u1eefa c\u00e1c ng\u00e0nh c\u00f4ng nghi\u1ec7p, ng\u01b0\u1eddi d\u00e2n v\u00e0 c\u1ed9ng \u0111\u1ed3ng.<\/p>\n<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_40 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" area-label=\"ez-toc-toggle-icon-1\"><label for=\"item-6ad18b3b83cf5\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;direction:ltr;\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input  type=\"checkbox\" id=\"item-6ad18b3b83cf5\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1 ' ><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/giao-diem-la-gi\/#Giao_diem_duong_thang_va_mat_phang\" title=\"Giao \u0111i\u1ec3m \u0111\u01b0\u1eddng th\u1eb3ng v\u00e0 m\u1eb7t ph\u1eb3ng\">Giao \u0111i\u1ec3m \u0111\u01b0\u1eddng th\u1eb3ng v\u00e0 m\u1eb7t ph\u1eb3ng<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/giao-diem-la-gi\/#Vi_du\" title=\"V\u00ed d\u1ee5:\">V\u00ed d\u1ee5:<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/giao-diem-la-gi\/#Duong_trung_tuyen_cua_tam_giac\" title=\"\u0110\u01b0\u1eddng trung tuy\u1ebfn c\u1ee7a tam gi\u00e1c\">\u0110\u01b0\u1eddng trung tuy\u1ebfn c\u1ee7a tam gi\u00e1c<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/giao-diem-la-gi\/#Tinh_chat\" title=\"T\u00ednh ch\u1ea5t:\">T\u00ednh ch\u1ea5t:<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/giao-diem-la-gi\/#Duong_trung_truc_cua_tam_giac\" title=\"\u0110\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a tam gi\u00e1c\">\u0110\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a tam gi\u00e1c<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-6\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/giao-diem-la-gi\/#Tinh_chat_cua_duong_trung_truc\" title=\"T\u00ednh ch\u1ea5t c\u1ee7a \u0111\u01b0\u1eddng trung tr\u1ef1c:\">T\u00ednh ch\u1ea5t c\u1ee7a \u0111\u01b0\u1eddng trung tr\u1ef1c:<\/a><ul class='ez-toc-list-level-4'><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-7\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/giao-diem-la-gi\/#Vi_du-2\" title=\"V\u00ed d\u1ee5:\">V\u00ed d\u1ee5:<\/a><\/li><\/ul><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-8\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/giao-diem-la-gi\/#Cac_dang_toan_ve_giao_diem_cua_hai_duong_thang\" title=\"C\u00e1c d\u1ea1ng to\u00e1n v\u1ec1 giao \u0111i\u1ec3m c\u1ee7a hai \u0111\u01b0\u1eddng th\u1eb3ng\">C\u00e1c d\u1ea1ng to\u00e1n v\u1ec1 giao \u0111i\u1ec3m c\u1ee7a hai \u0111\u01b0\u1eddng th\u1eb3ng<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-9\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/giao-diem-la-gi\/#Dang_toan_1_Tim_toa_do_giao_diem_cua_hai_duong_thang\" title=\"D\u1ea1ng to\u00e1n 1: T\u00ecm t\u1ecda \u0111\u1ed9 giao \u0111i\u1ec3m c\u1ee7a hai \u0111\u01b0\u1eddng th\u1eb3ng\">D\u1ea1ng to\u00e1n 1: T\u00ecm t\u1ecda \u0111\u1ed9 giao \u0111i\u1ec3m c\u1ee7a hai \u0111\u01b0\u1eddng th\u1eb3ng<\/a><ul class='ez-toc-list-level-4'><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-10\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/giao-diem-la-gi\/#Vi_du-3\" title=\"V\u00ed d\u1ee5:\">V\u00ed d\u1ee5:<\/a><\/li><\/ul><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-11\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/giao-diem-la-gi\/#Bai_tap_lien_quan_den_giao_diem_cua_hai_duong_thang\" title=\"B\u00e0i t\u1eadp li\u00ean quan \u0111\u1ebfn giao \u0111i\u1ec3m c\u1ee7a hai \u0111\u01b0\u1eddng th\u1eb3ng\">B\u00e0i t\u1eadp li\u00ean quan \u0111\u1ebfn giao \u0111i\u1ec3m c\u1ee7a hai \u0111\u01b0\u1eddng th\u1eb3ng<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-12\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/giao-diem-la-gi\/#Vi_du_bai_tap\" title=\"V\u00ed d\u1ee5 b\u00e0i t\u1eadp:\">V\u00ed d\u1ee5 b\u00e0i t\u1eadp:<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-13\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/giao-diem-la-gi\/#Dinh_nghia_cua_giao_diem\" title=\"\u0110\u1ecbnh ngh\u0129a c\u1ee7a giao \u0111i\u1ec3m\">\u0110\u1ecbnh ngh\u0129a c\u1ee7a giao \u0111i\u1ec3m<\/a><ul class='ez-toc-list-level-4'><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-14\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/giao-diem-la-gi\/#Tinh_chat_cua_giao_diem\" title=\"T\u00ednh ch\u1ea5t c\u1ee7a giao \u0111i\u1ec3m\">T\u00ednh ch\u1ea5t c\u1ee7a giao \u0111i\u1ec3m<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-15\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/giao-diem-la-gi\/#Dinh_nghia_cua_giao_diem-2\" title=\"\u0110\u1ecbnh ngh\u0129a c\u1ee7a giao \u0111i\u1ec3m\">\u0110\u1ecbnh ngh\u0129a c\u1ee7a giao \u0111i\u1ec3m<\/a><ul class='ez-toc-list-level-4'><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-16\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/giao-diem-la-gi\/#Tinh_chat_cua_giao_diem-2\" title=\"T\u00ednh ch\u1ea5t c\u1ee7a giao \u0111i\u1ec3m\">T\u00ednh ch\u1ea5t c\u1ee7a giao \u0111i\u1ec3m<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-17\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/giao-diem-la-gi\/#Dinh_nghia_cua_giao_diem-3\" title=\"\u0110\u1ecbnh ngh\u0129a c\u1ee7a giao \u0111i\u1ec3m\">\u0110\u1ecbnh ngh\u0129a c\u1ee7a giao \u0111i\u1ec3m<\/a><ul class='ez-toc-list-level-4'><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-18\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/giao-diem-la-gi\/#Tinh_chat_cua_giao_diem-3\" title=\"T\u00ednh ch\u1ea5t c\u1ee7a giao \u0111i\u1ec3m\">T\u00ednh ch\u1ea5t c\u1ee7a giao \u0111i\u1ec3m<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-19\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/giao-diem-la-gi\/#Dinh_nghia_cua_giao_diem-4\" title=\"\u0110\u1ecbnh ngh\u0129a c\u1ee7a giao \u0111i\u1ec3m\">\u0110\u1ecbnh ngh\u0129a c\u1ee7a giao \u0111i\u1ec3m<\/a><ul class='ez-toc-list-level-4'><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-20\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/giao-diem-la-gi\/#Tinh_chat_cua_giao_diem-4\" title=\"T\u00ednh ch\u1ea5t c\u1ee7a giao \u0111i\u1ec3m\">T\u00ednh ch\u1ea5t c\u1ee7a giao \u0111i\u1ec3m<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-21\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/giao-diem-la-gi\/#Dinh_nghia_cua_giao_diem-5\" title=\"\u0110\u1ecbnh ngh\u0129a c\u1ee7a giao \u0111i\u1ec3m\">\u0110\u1ecbnh ngh\u0129a c\u1ee7a giao \u0111i\u1ec3m<\/a><ul class='ez-toc-list-level-4'><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-22\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/giao-diem-la-gi\/#Tinh_chat_cua_giao_diem-5\" title=\"T\u00ednh ch\u1ea5t c\u1ee7a giao \u0111i\u1ec3m\">T\u00ednh ch\u1ea5t c\u1ee7a giao \u0111i\u1ec3m<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-23\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/giao-diem-la-gi\/#Dinh_nghia_cua_giao_diem-6\" title=\"\u0110\u1ecbnh ngh\u0129a c\u1ee7a giao \u0111i\u1ec3m\">\u0110\u1ecbnh ngh\u0129a c\u1ee7a giao \u0111i\u1ec3m<\/a><ul class='ez-toc-list-level-4'><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-24\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/giao-diem-la-gi\/#Tinh_chat_cua_giao_diem-6\" title=\"T\u00ednh ch\u1ea5t c\u1ee7a giao \u0111i\u1ec3m\">T\u00ednh ch\u1ea5t c\u1ee7a giao \u0111i\u1ec3m<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-25\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/giao-diem-la-gi\/#Dinh_nghia_cua_giao_diem-7\" title=\"\u0110\u1ecbnh ngh\u0129a c\u1ee7a giao \u0111i\u1ec3m\">\u0110\u1ecbnh ngh\u0129a c\u1ee7a giao \u0111i\u1ec3m<\/a><ul class='ez-toc-list-level-4'><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-26\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/giao-diem-la-gi\/#Tinh_chat_cua_giao_diem-7\" title=\"T\u00ednh ch\u1ea5t c\u1ee7a giao \u0111i\u1ec3m\">T\u00ednh ch\u1ea5t c\u1ee7a giao \u0111i\u1ec3m<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-27\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/giao-diem-la-gi\/#Dinh_nghia_cua_giao_diem-8\" title=\"\u0110\u1ecbnh ngh\u0129a c\u1ee7a giao \u0111i\u1ec3m\">\u0110\u1ecbnh ngh\u0129a c\u1ee7a giao \u0111i\u1ec3m<\/a><ul class='ez-toc-list-level-4'><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-28\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/giao-diem-la-gi\/#Tinh_chat_cua_giao_diem-8\" title=\"T\u00ednh ch\u1ea5t c\u1ee7a giao \u0111i\u1ec3m\">T\u00ednh ch\u1ea5t c\u1ee7a giao \u0111i\u1ec3m<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-29\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/giao-diem-la-gi\/#Dinh_nghia_cua_giao_diem-9\" title=\"\u0110\u1ecbnh ngh\u0129a c\u1ee7a giao \u0111i\u1ec3m\">\u0110\u1ecbnh ngh\u0129a c\u1ee7a giao \u0111i\u1ec3m<\/a><ul class='ez-toc-list-level-4'><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-30\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/giao-diem-la-gi\/#Tinh_chat_cua_giao_diem-9\" title=\"T\u00ednh ch\u1ea5t c\u1ee7a giao \u0111i\u1ec3m\">T\u00ednh ch\u1ea5t c\u1ee7a giao \u0111i\u1ec3m<\/a><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-31\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/giao-diem-la-gi\/#Dinh_nghia_giao_diem\" title=\"\u0110\u1ecbnh ngh\u0129a giao \u0111i\u1ec3m\">\u0110\u1ecbnh ngh\u0129a giao \u0111i\u1ec3m<\/a><ul class='ez-toc-list-level-4'><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-32\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/giao-diem-la-gi\/#Tinh_chat_cua_giao_diem-10\" title=\"T\u00ednh ch\u1ea5t c\u1ee7a giao \u0111i\u1ec3m\">T\u00ednh ch\u1ea5t c\u1ee7a giao \u0111i\u1ec3m<\/a><\/li><\/ul><\/li><\/ul><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-33\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/giao-diem-la-gi\/#Dinh_nghia_va_tinh_chat_cua_giao_diem\" title=\"\u0110\u1ecbnh ngh\u0129a v\u00e0 t\u00ednh ch\u1ea5t c\u1ee7a giao \u0111i\u1ec3m\">\u0110\u1ecbnh ngh\u0129a v\u00e0 t\u00ednh ch\u1ea5t c\u1ee7a giao \u0111i\u1ec3m<\/a><ul class='ez-toc-list-level-3'><li class='ez-toc-heading-level-3'><a class=\"ez-toc-link ez-toc-heading-34\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/giao-diem-la-gi\/#Dinh_nghia_giao_diem-2\" title=\"\u0110\u1ecbnh ngh\u0129a giao \u0111i\u1ec3m\">\u0110\u1ecbnh ngh\u0129a giao \u0111i\u1ec3m<\/a><ul class='ez-toc-list-level-4'><li class='ez-toc-heading-level-4'><a class=\"ez-toc-link ez-toc-heading-35\" href=\"https:\/\/ungdung.hotronghiencuu.com\/open\/giao-diem-la-gi\/#Tinh_chat_cua_giao_diem-11\" title=\"T\u00ednh ch\u1ea5t c\u1ee7a giao \u0111i\u1ec3m\">T\u00ednh ch\u1ea5t c\u1ee7a giao \u0111i\u1ec3m<\/a><\/li><\/ul><\/li><\/ul><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"Giao_diem_duong_thang_va_mat_phang\"><\/span>Giao \u0111i\u1ec3m \u0111\u01b0\u1eddng th\u1eb3ng v\u00e0 m\u1eb7t ph\u1eb3ng<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Trong kh\u00f4ng gian ba chi\u1ec1u, giao \u0111i\u1ec3m gi\u1eefa m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng v\u00e0 m\u1ed9t m\u1eb7t ph\u1eb3ng l\u00e0 \u0111i\u1ec3m chung c\u1ee7a c\u1ea3 hai. \u0110\u1ec3 t\u00ecm giao \u0111i\u1ec3m n\u00e0y, ta c\u1ea7n gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh c\u1ee7a \u0111\u01b0\u1eddng th\u1eb3ng v\u00e0 m\u1eb7t ph\u1eb3ng.<\/p>\n<p>\u0110\u1ed1i v\u1edbi \u0111\u01b0\u1eddng th\u1eb3ng c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh ax + by + cz + d = 0 v\u00e0 m\u1eb7t ph\u1eb3ng c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh Ax + By + Cz + D = 0, ta gi\u1ea3i h\u1ec7 c\u00e1c ph\u01b0\u01a1ng tr\u00ecnh n\u00e0y \u0111\u1ec3 t\u00ecm ra gi\u00e1 tr\u1ecb c\u1ee7a x, y, z. N\u1ebfu t\u1ed3n t\u1ea1i duy nh\u1ea5t m\u1ed9t nghi\u1ec7m (x0, y0, z0), th\u00ec \u0111i\u1ec3m (x0, y0, z0) ch\u00ednh l\u00e0 giao \u0111i\u1ec3m c\u1ee7a \u0111\u01b0\u1eddng th\u1eb3ng v\u00e0 m\u1eb7t ph\u1eb3ng.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Vi_du\"><\/span>V\u00ed d\u1ee5:<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>T\u00ecm giao \u0111i\u1ec3m c\u1ee7a \u0111\u01b0\u1eddng th\u1eb3ng c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh x &#8211; 2y + z = 4 v\u00e0 m\u1eb7t ph\u1eb3ng c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh 2x &#8211; y + 3z = 5.<\/p>\n<p>Gi\u1ea3i h\u1ec7 c\u00e1c ph\u01b0\u01a1ng tr\u00ecnh:<\/p>\n<ul>\n<li>x &#8211; 2y + z = 4<\/li>\n<li>2x &#8211; y + 3z = 5<\/li>\n<\/ul>\n<p>Ta c\u00f3 th\u1ec3 gi\u1ea3i h\u1ec7 n\u00e0y b\u1eb1ng ph\u01b0\u01a1ng ph\u00e1p \u0111\u1ea1i s\u1ed1 th\u00f4ng th\u01b0\u1eddng ho\u1eb7c s\u1eed d\u1ee5ng c\u00e1c c\u00f4ng th\u1ee9c Cramer. Sau khi gi\u1ea3i, ta t\u00ecm \u0111\u01b0\u1ee3c gi\u00e1 tr\u1ecb c\u1ee7a x, y, z l\u00e0 (2, 1, 1). V\u1eady giao \u0111i\u1ec3m c\u1ee7a \u0111\u01b0\u1eddng th\u1eb3ng v\u00e0 m\u1eb7t ph\u1eb3ng l\u00e0 \u0111i\u1ec3m (2, 1, 1).<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Duong_trung_tuyen_cua_tam_giac\"><\/span>\u0110\u01b0\u1eddng trung tuy\u1ebfn c\u1ee7a tam gi\u00e1c<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>\u0110\u01b0\u1eddng trung tuy\u1ebfn c\u1ee7a m\u1ed9t tam gi\u00e1c l\u00e0 \u0111o\u1ea1n th\u1eb3ng n\u1ed1i trung \u0111i\u1ec3m c\u1ee7a hai c\u1ea1nh b\u1ea5t k\u1ef3 v\u1edbi nhau. \u0110\u01b0\u1eddng trung tuy\u1ebfn lu\u00f4n \u0111i qua tr\u1ecdng t\u00e2m c\u1ee7a tam gi\u00e1c.<\/p>\n<p>Trong tam gi\u00e1c ABC c\u00f3 tr\u1ecdng t\u00e2m G v\u00e0 c\u00e1c \u0111i\u1ec3m M, N l\u1ea7n l\u01b0\u1ee3t l\u00e0 trung \u0111i\u1ec3m c\u1ee7a AB v\u00e0 AC. \u0110\u01b0\u1eddng th\u1eb3ng MN \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 \u0111\u01b0\u1eddng trung tuy\u1ebfn c\u1ee7a tam gi\u00e1c ABC.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Tinh_chat\"><\/span>T\u00ednh ch\u1ea5t:<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<ul>\n<li>\u0110\u01b0\u1eddng trung tuy\u1ebfn lu\u00f4n \u0111i qua tr\u1ecdng t\u00e2m G.<\/li>\n<li>\u0110\u1ed9 d\u00e0i \u0111o\u1ea1n MN b\u1eb1ng m\u1ed9t n\u1eeda \u0111\u1ed9 d\u00e0i c\u1ea1nh BC.<\/li>\n<li>\u0110\u01b0\u1eddng trung tuy\u1ebfn song song v\u1edbi c\u1ea1nh AB v\u00e0 c\u00f3 \u0111\u1ed9 d\u00e0i b\u1eb1ng m\u1ed9t n\u1eeda c\u1ea1nh AB.<\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"Duong_trung_truc_cua_tam_giac\"><\/span>\u0110\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a tam gi\u00e1c<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><img decoding=\"async\" alt=\"\u0110\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a tam gi\u00e1c\" src=\"https:\/\/ungdung.hotronghiencuu.com\/open\/wp-content\/uploads\/2023\/09\/giao_diem_dinh_nghia_thuat_ngu_va_tinh_chat.jpg\" style=\"text-align: center; clear: both; display: block; margin: 0 auto;\" title=\"\u0110\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a tam gi\u00e1c\"\/><\/p>\n<p>\u0110\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a tam gi\u00e1c l\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng \u0111i qua trung \u0111i\u1ec3m c\u1ee7a m\u1ed9t c\u1ea1nh v\u00e0 vu\u00f4ng g\u00f3c v\u1edbi c\u1ea1nh \u0111\u00f3. \u0110\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a tam gi\u00e1c c\u00f3 vai tr\u00f2 quan tr\u1ecdng trong vi\u1ec7c x\u00e1c \u0111\u1ecbnh c\u00e1c \u0111\u1ec9nh, t\u00e2m v\u00e0 c\u00e1c \u0111\u01b0\u1eddng cao c\u1ee7a tam gi\u00e1c.<\/p>\n<p>C\u1ee5 th\u1ec3, \u0111\u1ec3 v\u1ebd \u0111\u01b0\u1ee3c \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a m\u1ed9t c\u1ea1nh AB, ta ch\u1ec9 c\u1ea7n l\u1ea5y hai \u0111i\u1ec3m A&#8217; v\u00e0 B&#8217; n\u1eb1m \u1edf hai ph\u00eda c\u1ea1nh AB sao cho AA&#8217; = BB&#8217; = 1\/2 AB. Khi \u0111\u00f3, \u0111\u01b0\u1eddng th\u1eb3ng A&#8217;B&#8217; ch\u00ednh l\u00e0 \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a c\u1ea1nh AB.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Tinh_chat_cua_duong_trung_truc\"><\/span>T\u00ednh ch\u1ea5t c\u1ee7a \u0111\u01b0\u1eddng trung tr\u1ef1c:<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<ul>\n<li>\u0110\u1ed1i x\u1ee9ng qua \u0111\u01b0\u1eddng trung b\u00ecnh: \u0110i\u1ec3m giao nhau c\u1ee7a c\u00e1c \u0111\u01b0\u1eddng trung b\u00ecnh trong tam gi\u00e1c ch\u00ednh l\u00e0 t\u00e2m c\u1ee7a tam gi\u00e1c.<\/li>\n<li>Vu\u00f4ng g\u00f3c v\u1edbi c\u1ea1nh: \u0110\u01b0\u1eddng trung tr\u1ef1c lu\u00f4n vu\u00f4ng g\u00f3c v\u1edbi c\u1ea1nh m\u00e0 n\u00f3 \u0111i qua.<\/li>\n<li>Giao \u0111i\u1ec3m: C\u00e1c \u0111\u01b0\u1eddng trung b\u00ecnh trong tam gi\u00e1c giao nhau t\u1ea1i m\u1ed9t \u0111i\u1ec3m duy nh\u1ea5t, \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 t\u00e2m trong.<\/li>\n<\/ul>\n<h4><span class=\"ez-toc-section\" id=\"Vi_du-2\"><\/span>V\u00ed d\u1ee5:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>H\u00e3y x\u00e1c \u0111\u1ecbnh \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a tam gi\u00e1c ABC v\u1edbi A(2, 3), B(6, 5) v\u00e0 C(8, 1).<\/p>\n<p>\u0110\u1ec3 x\u00e1c \u0111\u1ecbnh \u0111\u01b0\u1ee3c \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a c\u1ea1nh AB, ta c\u1ea7n t\u00ecm \u0111i\u1ec3m n\u1eb1m \u1edf gi\u1eefa hai \u0111i\u1ec3m A v\u00e0 B. Ta c\u00f3:<\/p>\n<ul>\n<li>T\u1ecda \u0111\u1ed9 x c\u1ee7a \u0111i\u1ec3m n\u1eb1m gi\u1eefa A v\u00e0 B: (2 + 6)\/2 = 4<\/li>\n<li>T\u1ecda \u0111\u1ed9 y c\u1ee7a \u0111i\u1ec3m n\u1eb1m gi\u1eefa A v\u00e0 B: (3 + 5)\/2 = 4<\/li>\n<\/ul>\n<p>V\u1eady, ta c\u00f3 \u0111i\u1ec3m trung b\u00ecnh M(4, 4). \u0110\u01b0\u1eddng th\u1eb3ng qua M v\u00e0 vu\u00f4ng g\u00f3c v\u1edbi AB ch\u00ednh l\u00e0 \u0111\u01b0\u1eddng trung tr\u1ef1c c\u1ee7a c\u1ea1nh AB.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Cac_dang_toan_ve_giao_diem_cua_hai_duong_thang\"><\/span>C\u00e1c d\u1ea1ng to\u00e1n v\u1ec1 giao \u0111i\u1ec3m c\u1ee7a hai \u0111\u01b0\u1eddng th\u1eb3ng<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Giao \u0111i\u1ec3m c\u1ee7a hai \u0111\u01b0\u1eddng th\u1eb3ng l\u00e0 \u0111i\u1ec3m m\u00e0 hai \u0111\u01b0\u1eddng th\u1eb3ng c\u1eaft nhau ho\u1eb7c song song nhau. Trong to\u00e1n h\u1ecdc, c\u00f3 nhi\u1ec1u d\u1ea1ng to\u00e1n li\u00ean quan \u0111\u1ebfn vi\u1ec7c t\u00ecm giao \u0111i\u1ec3m c\u1ee7a hai \u0111\u01b0\u1eddng th\u1eb3ng, t\u1eeb vi\u1ec7c t\u00ednh to\u00e1n t\u1ecda \u0111\u1ed9 giao \u0111i\u1ec3m cho t\u1edbi vi\u1ec7c x\u00e1c \u0111\u1ecbnh c\u00e1c t\u00ednh ch\u1ea5t hay quy lu\u1eadt li\u00ean quan.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Dang_toan_1_Tim_toa_do_giao_diem_cua_hai_duong_thang\"><\/span>D\u1ea1ng to\u00e1n 1: T\u00ecm t\u1ecda \u0111\u1ed9 giao \u0111i\u1ec3m c\u1ee7a hai \u0111\u01b0\u1eddng th\u1eb3ng<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>\u0110\u1ec3 t\u00ecm t\u1ecda \u0111\u1ed9 giao \u0111i\u1ec3m c\u1ee7a hai \u0111\u01b0\u1eddng th\u1eb3ng, ta c\u1ea7n gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh tuy\u1ebfn t\u00ednh v\u1edbi hai ph\u01b0\u01a1ng tr\u00ecnh c\u1ee7a c\u00e1c \u0111\u01b0\u1eddng th\u1eb3ng. H\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh n\u00e0y s\u1ebd cho ta gi\u00e1 tr\u1ecb x v\u00e0 y ch\u00ednh l\u00e0 t\u1ecda \u0111\u1ed9 c\u1ee7a \u0111i\u1ec3m giao \u0111i\u1ec3m.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"Vi_du-3\"><\/span>V\u00ed d\u1ee5:<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>T\u00ecm t\u1ecda \u0111\u1ed9 giao \u0111i\u1ec3m c\u1ee7a hai \u0111\u01b0\u1eddng th\u1eb3ng c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: 2x + 3y = 7 v\u00e0 5x &#8211; y = 1.<\/p>\n<p>Gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh:<\/p>\n<ul>\n<li>2x + 3y = 7<\/li>\n<li>5x &#8211; y = 1<\/li>\n<\/ul>\n<p>T\u1eeb \u0111\u00f3, ta c\u00f3 th\u1ec3 suy ra gi\u00e1 tr\u1ecb x v\u00e0 y ch\u00ednh l\u00e0 t\u1ecda \u0111\u1ed9 c\u1ee7a \u0111i\u1ec3m giao \u0111i\u1ec3m.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Bai_tap_lien_quan_den_giao_diem_cua_hai_duong_thang\"><\/span>B\u00e0i t\u1eadp li\u00ean quan \u0111\u1ebfn giao \u0111i\u1ec3m c\u1ee7a hai \u0111\u01b0\u1eddng th\u1eb3ng<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>B\u00e0i t\u1eadp li\u00ean quan \u0111\u1ebfn giao \u0111i\u1ec3m c\u1ee7a hai \u0111\u01b0\u1eddng th\u1eb3ng gi\u00fap r\u00e8n luy\u1ec7n kh\u1ea3 n\u0103ng gi\u1ea3i quy\u1ebft v\u1ea5n \u0111\u1ec1, \u00e1p d\u1ee5ng ki\u1ebfn th\u1ee9c v\u1ec1 h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh tuy\u1ebfn t\u00ednh v\u00e0 t\u00ednh to\u00e1n c\u00e1c th\u00f4ng s\u1ed1 trong kh\u00f4ng gian. C\u00e1c b\u00e0i t\u1eadp n\u00e0y c\u00f3 th\u1ec3 y\u00eau c\u1ea7u t\u00ecm t\u1ecda \u0111\u1ed9 giao \u0111i\u1ec3m, x\u00e1c \u0111\u1ecbnh t\u00ednh ch\u1ea5t c\u1ee7a giao \u0111i\u1ec3m hay gi\u1ea3i quy\u1ebft c\u00e1c b\u00e0i to\u00e1n th\u1ef1c t\u1ebf li\u00ean quan \u0111\u1ebfn hai \u0111\u01b0\u1eddng th\u1eb3ng.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Vi_du_bai_tap\"><\/span>V\u00ed d\u1ee5 b\u00e0i t\u1eadp:<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Cho hai \u0111\u01b0\u1eddng th\u1eb3ng c\u00f3 ph\u01b0\u01a1ng tr\u00ecnh: 2x + 3y = 7 v\u00e0 5x &#8211; y = 1. H\u00e3y x\u00e1c \u0111\u1ecbnh t\u1ecda \u0111\u1ed9 giao \u0111i\u1ec3m v\u00e0 t\u00ednh di\u1ec7n t\u00edch h\u00ecnh tam gi\u00e1c ABC v\u1edbi A(0,0), B(2,4) v\u00e0 C l\u00e0 giao \u0111i\u1ec3m c\u1ee7a hai \u0111\u01b0\u1eddng th\u1eb3ng.<\/p>\n<p>Gi\u1ea3i:<\/p>\n<ul>\n<li>T\u00ecm t\u1ecda \u0111\u1ed9 giao \u0111i\u1ec3m c\u1ee7a hai \u0111\u01b0\u1eddng th\u1eb3ng theo ph\u1ea7n tr\u01b0\u1edbc.<\/li>\n<li>Sau khi x\u00e1c \u0111\u1ecbnh \u0111\u01b0\u1ee3c t\u1ecda \u0111\u1ed9 giao \u0111i\u1ec3m, ta c\u00f3 A(0,0), B(2,4) v\u00e0 C(t\u1ecda \u0111\u1ed9 giao \u0111i\u1ec3m).<\/li>\n<li>T\u00ednh di\u1ec7n t\u00edch h\u00ecnh tam gi\u00e1c ABC b\u1eb1ng c\u00f4ng th\u1ee9c di\u1ec7n t\u00edch tam gi\u00e1c: S = (1\/2) * |x1(y2-y3) + x2(y3-y1) + x3(y1-y2)|<\/li>\n<\/ul>\n<h3><span class=\"ez-toc-section\" id=\"Dinh_nghia_cua_giao_diem\"><\/span>\u0110\u1ecbnh ngh\u0129a c\u1ee7a giao \u0111i\u1ec3m<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Giao \u0111i\u1ec3m l\u00e0 \u0111i\u1ec3m chung c\u1ee7a hai hay nhi\u1ec1u \u0111\u1ed1i t\u01b0\u1ee3ng, v\u1eadt th\u1ec3 ho\u1eb7c h\u1ec7 th\u1ed1ng. Trong to\u00e1n h\u1ecdc, giao \u0111i\u1ec3m th\u01b0\u1eddng \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 ch\u1ec9 s\u1ef1 c\u1eaft nhau c\u1ee7a c\u00e1c \u0111\u01b0\u1eddng th\u1eb3ng, \u0111\u01b0\u1eddng cong ho\u1eb7c c\u00e1c h\u00ecnh h\u1ecdc kh\u00e1c. Giao \u0111i\u1ec3m c\u00f3 th\u1ec3 l\u00e0 m\u1ed9t \u0111i\u1ec3m duy nh\u1ea5t ho\u1eb7c m\u1ed9t t\u1eadp h\u1ee3p c\u00e1c \u0111i\u1ec3m.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"Tinh_chat_cua_giao_diem\"><\/span>T\u00ednh ch\u1ea5t c\u1ee7a giao \u0111i\u1ec3m<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>&#8211; Giao \u0111i\u1ec3m c\u1ee7a hai \u0111\u01b0\u1eddng th\u1eb3ng song song kh\u00f4ng t\u1ed3n t\u1ea1i.<br \/>\n&#8211; Giao \u0111i\u1ec3m c\u1ee7a hai \u0111\u01b0\u1eddng th\u1eb3ng c\u1eaft nhau ch\u1ec9 c\u00f3 duy nh\u1ea5t m\u1ed9t \u0111i\u1ec3m.<br \/>\n&#8211; Giao \u0111i\u1ec3m c\u1ee7a hai \u0111\u01b0\u1eddng cong c\u00f3 th\u1ec3 l\u00e0 m\u1ed9t ho\u1eb7c nhi\u1ec1u \u0111i\u1ec3m.<br \/>\n&#8211; Giao \u0111i\u1ec3m c\u1ee7a hai h\u00ecnh vu\u00f4ng l\u00e0 m\u1ed9t t\u1eadp h\u1ee3p c\u00e1c c\u1ea1nh chung.<br \/>\n&#8211; Giao \u0111i\u1ec3m c\u1ee7a hai h\u00ecnh tr\u00f2n c\u00f3 th\u1ec3 l\u00e0 m\u1ed9t ho\u1eb7c hai \u0111i\u1ec3m.<\/p>\n<p>D\u01b0\u1edbi \u0111\u00e2y l\u00e0 v\u00ed d\u1ee5 v\u1ec1 t\u00ednh ch\u1ea5t giao \u0111i\u1ec3m trong h\u00ecnh \u1ea3nh:<\/p>\n<p><img decoding=\"async\" alt=\"V\u00ed d\u1ee5 v\u1ec1 t\u00ednh ch\u1ea5t giao \u0111i\u1ec3m\" src=\"intersection_example.png\"\/><\/p>\n<p>Trong v\u00ed d\u1ee5 n\u00e0y, ta c\u00f3 hai \u0111\u01b0\u1eddng th\u1eb3ng AB v\u00e0 CD. \u0110i\u1ec3m E l\u00e0 giao \u0111i\u1ec3m gi\u1eefa AB v\u00e0 CD. Ta c\u0169ng c\u00f3 ba h\u00ecnh tr\u00f2n DEF, FGH v\u00e0 IJK. Giao \u0111i\u1ec3m c\u1ee7a hai h\u00ecnh tr\u00f2n DEF v\u00e0 FGH l\u00e0 \u0111i\u1ec3m F.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Dinh_nghia_cua_giao_diem-2\"><\/span>\u0110\u1ecbnh ngh\u0129a c\u1ee7a giao \u0111i\u1ec3m<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Giao \u0111i\u1ec3m l\u00e0 \u0111i\u1ec3m chung c\u1ee7a hai ho\u1eb7c nhi\u1ec1u \u0111\u1ed1i t\u01b0\u1ee3ng, \u0111\u01b0\u1eddng th\u1eb3ng, \u0111\u01b0\u1eddng cong, hay h\u00ecnh h\u1ecdc kh\u00e1c. Khi hai \u0111\u1ed1i t\u01b0\u1ee3ng c\u1eaft nhau ho\u1eb7c ti\u1ebfp x\u00fac v\u1edbi nhau t\u1ea1i m\u1ed9t \u0111i\u1ec3m duy nh\u1ea5t, ta g\u1ecdi \u0111i\u1ec3m \u0111\u00f3 l\u00e0 giao \u0111i\u1ec3m. Giao \u0111i\u1ec3m c\u00f3 th\u1ec3 l\u00e0 m\u1ed9t \u0111i\u1ec3m trong kh\u00f4ng gian ba chi\u1ec1u ho\u1eb7c tr\u00ean m\u1ed9t m\u1eb7t ph\u1eb3ng.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"Tinh_chat_cua_giao_diem-2\"><\/span>T\u00ednh ch\u1ea5t c\u1ee7a giao \u0111i\u1ec3m<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>1. T\u00ednh duy nh\u1ea5t: M\u1ed7i c\u1eb7p \u0111\u1ed1i t\u01b0\u1ee3ng ch\u1ec9 c\u00f3 th\u1ec3 c\u00f3 m\u1ed9t giao \u0111i\u1ec3m duy nh\u1ea5t. N\u1ebfu c\u00f3 nhi\u1ec1u h\u01a1n m\u1ed9t \u0111i\u1ec3m chung, ch\u00fang s\u1ebd \u0111\u01b0\u1ee3c coi l\u00e0 c\u00e1c giao \u0111i\u1ec3m ri\u00eang bi\u1ec7t.<br \/>\n2. T\u00ednh c\u00e2n x\u1ee9ng: N\u1ebfu hai \u0111\u1ed1i t\u01b0\u1ee3ng c\u1eaft nhau t\u1ea1i m\u1ed9t giao \u0111i\u1ec3m, th\u00ec giao \u0111i\u1ec3m n\u00e0y s\u1ebd n\u1eb1m \u1edf gi\u1eefa kho\u1ea3ng c\u00e1ch gi\u1eefa c\u00e1c \u0111\u1ec9nh c\u1ee7a hai \u0111\u1ed1i t\u01b0\u1ee3ng.<br \/>\n3. T\u00ednh li\u00ean t\u1ee5c: Khi c\u00e1c \u0111\u1ed1i t\u01b0\u1ee3ng di chuy\u1ec3n d\u1ea7n d\u1ea7n v\u00e0 ti\u1ebfp t\u1ee5c ti\u1ebfp x\u00fac ho\u1eb7c c\u1eaft nhau, v\u1ecb tr\u00ed c\u1ee7a giao \u0111i\u1ec3m s\u1ebd thay \u0111\u1ed5i theo quy lu\u1eadt li\u00ean t\u1ee5c.<\/p>\n<p>D\u01b0\u1edbi \u0111\u00e2y l\u00e0 m\u1ed9t s\u1ed1 v\u00ed d\u1ee5 v\u1ec1 giao \u0111i\u1ec3m:<br \/>\n&#8211; Hai \u0111\u01b0\u1eddng th\u1eb3ng c\u1eaft nhau t\u1ea1i m\u1ed9t \u0111i\u1ec3m duy nh\u1ea5t.<br \/>\n&#8211; M\u1ed9t \u0111\u01b0\u1eddng tr\u00f2n v\u00e0 m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng c\u00f3 th\u1ec3 c\u1eaft nhau t\u1ea1i hai \u0111i\u1ec3m.<br \/>\n&#8211; Hai \u0111\u01b0\u1eddng cong c\u00f3 th\u1ec3 c\u00f3 nhi\u1ec1u \u0111i\u1ec3m chung, t\u00f9y thu\u1ed9c v\u00e0o h\u00ecnh d\u1ea1ng c\u1ee7a ch\u00fang.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Dinh_nghia_cua_giao_diem-3\"><\/span>\u0110\u1ecbnh ngh\u0129a c\u1ee7a giao \u0111i\u1ec3m<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Giao \u0111i\u1ec3m l\u00e0 \u0111i\u1ec3m ho\u1eb7c v\u1ecb tr\u00ed m\u00e0 hai hay nhi\u1ec1u \u0111\u1ed1i t\u01b0\u1ee3ng, \u0111\u01b0\u1eddng th\u1eb3ng, \u0111\u01b0\u1eddng cong ho\u1eb7c h\u00ecnh d\u1ea1ng c\u1eaft nhau. Khi hai \u0111\u1ed1i t\u01b0\u1ee3ng c\u1eaft nhau t\u1ea1i m\u1ed9t \u0111i\u1ec3m duy nh\u1ea5t, ta g\u1ecdi \u0111i\u1ec3m \u0111\u00f3 l\u00e0 giao \u0111i\u1ec3m c\u1ee7a ch\u00fang. Giao \u0111i\u1ec3m c\u00f3 th\u1ec3 l\u00e0 m\u1ed9t \u0111i\u1ec3m trong kh\u00f4ng gian ba chi\u1ec1u ho\u1eb7c tr\u00ean m\u1ed9t m\u1eb7t ph\u1eb3ng hai chi\u1ec1u.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"Tinh_chat_cua_giao_diem-3\"><\/span>T\u00ednh ch\u1ea5t c\u1ee7a giao \u0111i\u1ec3m<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>&#8211; M\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng c\u00f3 th\u1ec3 c\u1eaft m\u1ed9t \u0111\u01b0\u1eddng cong t\u1ea1i kh\u00f4ng qu\u00e1 hai \u0111i\u1ec3m. N\u1ebfu s\u1ed1 l\u01b0\u1ee3ng giao \u0111i\u1ec3m gi\u1eefa m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng v\u00e0 m\u1ed9t \u0111\u01b0\u1eddng cong l\u1edbn h\u01a1n hai, t\u1ee9c l\u00e0 ch\u00fang c\u00f3 \u00edt nh\u1ea5t m\u1ed9t ph\u1ea7n chung.<br \/>\n&#8211; Hai \u0111\u01b0\u1eddng th\u1eb3ng song song s\u1ebd kh\u00f4ng bao gi\u1edd c\u1eaft nhau v\u00e0 do \u0111\u00f3 kh\u00f4ng c\u00f3 giao \u0111i\u1ec3m.<br \/>\n&#8211; M\u1ed9t h\u00ecnh vu\u00f4ng c\u00f3 b\u1ed1n g\u00f3c vu\u00f4ng v\u00e0 b\u1ed1n c\u1ea1nh b\u1eb1ng nhau. Do \u0111\u00f3, c\u00e1c \u0111\u01b0\u1eddng ch\u00e9o trong h\u00ecnh vu\u00f4ng s\u1ebd c\u1eaft nhau t\u1ea1i trung \u0111i\u1ec3m c\u1ee7a ch\u00fang, v\u00e0 v\u00ec v\u1eady, h\u00ecnh vu\u00f4ng c\u00f3 hai giao \u0111i\u1ec3m tr\u00ean c\u00e1c \u0111\u01b0\u1eddng ch\u00e9o.<br \/>\n&#8211; Trong kh\u00f4ng gian ba chi\u1ec1u, khi hai m\u1eb7t ph\u1eb3ng c\u1eaft nhau, ch\u00fang t\u1ea1o ra m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng g\u1ecdi l\u00e0 \u0111\u01b0\u1eddng c\u1eaft. \u0110\u01b0\u1eddng c\u1eaft n\u00e0y s\u1ebd c\u00f3 v\u00f4 s\u1ed1 \u0111i\u1ec3m giao \u0111i\u1ec3m tr\u00ean n\u00f3, t\u01b0\u01a1ng \u1ee9ng v\u1edbi c\u00e1c \u0111i\u1ec3m n\u1eb1m tr\u00ean \u0111\u01b0\u1eddng c\u1eaft c\u1ee7a hai m\u1eb7t ph\u1eb3ng.<\/p>\n<p>D\u01b0\u1edbi \u0111\u00e2y l\u00e0 danh s\u00e1ch c\u00e1c t\u00ednh ch\u1ea5t chung c\u1ee7a giao \u0111i\u1ec3m:<br \/>\n&#8211; Giao \u0111i\u1ec3m c\u00f3 th\u1ec3 l\u00e0 m\u1ed9t \u0111i\u1ec3m duy nh\u1ea5t, m\u1ed9t \u0111o\u1ea1n th\u1eb3ng, ho\u1eb7c m\u1ed9t h\u00ecnh d\u1ea1ng ph\u1ee9c t\u1ea1p h\u01a1n.<br \/>\n&#8211; C\u00e1c giao \u0111i\u1ec3m c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh b\u1eb1ng c\u00e1ch gi\u1ea3i h\u1ec7 ph\u01b0\u01a1ng tr\u00ecnh ho\u1eb7c s\u1eed d\u1ee5ng c\u00f4ng c\u1ee5 h\u00ecnh h\u1ecdc.<br \/>\n&#8211; S\u1ed1 l\u01b0\u1ee3ng v\u00e0 v\u1ecb tr\u00ed c\u1ee7a c\u00e1c giao \u0111i\u1ec3m ph\u1ee5 thu\u1ed9c v\u00e0o t\u00ednh ch\u1ea5t v\u00e0 v\u1ecb tr\u00ed c\u1ee7a c\u00e1c \u0111\u1ed1i t\u01b0\u1ee3ng li\u00ean quan.<br \/>\n&#8211; Giao \u0111i\u1ec3m c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 gi\u1ea3i quy\u1ebft c\u00e1c b\u00e0i to\u00e1n trong h\u00ecnh h\u1ecdc v\u00e0 to\u00e1n h\u1ecdc \u1ee9ng d\u1ee5ng kh\u00e1c.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Dinh_nghia_cua_giao_diem-4\"><\/span>\u0110\u1ecbnh ngh\u0129a c\u1ee7a giao \u0111i\u1ec3m<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Giao \u0111i\u1ec3m l\u00e0 \u0111i\u1ec3m chung c\u1ee7a hai ho\u1eb7c nhi\u1ec1u \u0111\u1ed1i t\u01b0\u1ee3ng, h\u00ecnh d\u1ea1ng ho\u1eb7c \u0111\u01b0\u1eddng th\u1eb3ng. Trong kh\u00f4ng gian hai chi\u1ec1u, giao \u0111i\u1ec3m \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh b\u1edfi t\u1ecda \u0111\u1ed9 (x, y) v\u00e0 c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c bi\u1ec3u di\u1ec5n tr\u00ean m\u1eb7t ph\u1eb3ng. Trong kh\u00f4ng gian ba chi\u1ec1u, giao \u0111i\u1ec3m \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh b\u1edfi t\u1ecda \u0111\u1ed9 (x, y, z) v\u00e0 c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c bi\u1ec3u di\u1ec5n trong kh\u00f4ng gian ba chi\u1ec1u.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"Tinh_chat_cua_giao_diem-4\"><\/span>T\u00ednh ch\u1ea5t c\u1ee7a giao \u0111i\u1ec3m<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>1. T\u00ednh duy nh\u1ea5t: Giao \u0111i\u1ec3m gi\u1eefa hai \u0111\u1ed1i t\u01b0\u1ee3ng l\u00e0 duy nh\u1ea5t v\u00e0 ch\u1ec9 t\u1ed3n t\u1ea1i m\u1ed9t \u0111i\u1ec3m chung duy nh\u1ea5t.<br \/>\n2. T\u00ednh ph\u1ee5 thu\u1ed9c: S\u1ef1 t\u1ed3n t\u1ea1i c\u1ee7a m\u1ed9t giao \u0111i\u1ec3m ph\u1ee5 thu\u1ed9c v\u00e0o c\u00e1c t\u00ednh ch\u1ea5t v\u00e0 v\u1ecb tr\u00ed c\u1ee7a c\u00e1c \u0111\u1ed1i t\u01b0\u1ee3ng li\u00ean quan. N\u1ebfu hai \u0111\u1ed1i t\u01b0\u1ee3ng kh\u00f4ng c\u1eaft nhau ho\u1eb7c kh\u00f4ng c\u00f3 s\u1ef1 ti\u1ebfp x\u00fac, th\u00ec kh\u00f4ng c\u00f3 giao \u0111i\u1ec3m gi\u1eefa ch\u00fang.<br \/>\n3. T\u00ednh kh\u1ea3 thi: Giao \u0111i\u1ec3m c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c t\u00ednh to\u00e1n v\u00e0 x\u00e1c \u0111\u1ecbnh b\u1eb1ng c\u00e1ch s\u1eed d\u1ee5ng c\u00e1c c\u00f4ng th\u1ee9c v\u00e0 ph\u01b0\u01a1ng ph\u00e1p to\u00e1n h\u1ecdc ph\u00f9 h\u1ee3p.<br \/>\n4. T\u00ednh \u1ee9ng d\u1ee5ng: Giao \u0111i\u1ec3m \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng r\u1ed9ng r\u00e3i trong c\u00e1c l\u0129nh v\u1ef1c nh\u01b0 h\u00ecnh h\u1ecdc, \u0111\u1ed3 h\u1ecda m\u00e1y t\u00ednh, thi\u1ebft k\u1ebf v\u00e0 x\u1eed l\u00fd \u1ea3nh \u0111\u1ec3 t\u00ecm ra v\u1ecb tr\u00ed chung c\u1ee7a c\u00e1c \u0111\u1ed1i t\u01b0\u1ee3ng ho\u1eb7c \u0111i\u1ec3m g\u1eb7p nhau c\u1ee7a c\u00e1c \u0111\u01b0\u1eddng th\u1eb3ng.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Dinh_nghia_cua_giao_diem-5\"><\/span>\u0110\u1ecbnh ngh\u0129a c\u1ee7a giao \u0111i\u1ec3m<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Giao \u0111i\u1ec3m l\u00e0 \u0111i\u1ec3m chung c\u1ee7a hai hay nhi\u1ec1u \u0111\u1ed1i t\u01b0\u1ee3ng, \u0111\u01b0\u1eddng th\u1eb3ng, ho\u1eb7c h\u00ecnh h\u1ecdc kh\u00e1c nhau. Khi hai \u0111\u1ed1i t\u01b0\u1ee3ng c\u1eaft nhau ho\u1eb7c giao nhau t\u1ea1i m\u1ed9t \u0111i\u1ec3m duy nh\u1ea5t, ta g\u1ecdi \u0111i\u1ec3m \u0111\u00f3 l\u00e0 giao \u0111i\u1ec3m. Giao \u0111i\u1ec3m c\u00f3 th\u1ec3 l\u00e0 m\u1ed9t \u0111i\u1ec3m tr\u00ean m\u1eb7t ph\u1eb3ng, trong kh\u00f4ng gian ba chi\u1ec1u, ho\u1eb7c tr\u00ean b\u1ec1 m\u1eb7t c\u00e1c h\u00ecnh h\u1ecdc kh\u00e1c nh\u01b0 c\u1ea7u, h\u00ecnh c\u1ea7u v\u00e0 t\u1ee9 di\u1ec7n.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"Tinh_chat_cua_giao_diem-5\"><\/span>T\u00ednh ch\u1ea5t c\u1ee7a giao \u0111i\u1ec3m<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>&#8211; Giao \u0111i\u1ec3m gi\u1eefa hai \u0111\u01b0\u1eddng th\u1eb3ng: N\u1ebfu hai \u0111\u01b0\u1eddng th\u1eb3ng kh\u00f4ng song song v\u00e0 kh\u00f4ng tr\u00f9ng nhau, ch\u00fang s\u1ebd c\u00f3 m\u1ed9t giao \u0111i\u1ec3m duy nh\u1ea5t.<br \/>\n&#8211; Giao \u0111i\u1ec3m gi\u1eefa \u0111\u01b0\u1eddng th\u1eb3ng v\u00e0 m\u1eb7t ph\u1eb3ng: M\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng c\u00f3 th\u1ec3 c\u1eaft qua ho\u1eb7c song song v\u1edbi m\u1ed9t m\u1eb7t ph\u1eb3ng. Trong tr\u01b0\u1eddng h\u1ee3p c\u1eaft qua, ch\u00fang s\u1ebd c\u00f3 m\u1ed9t giao \u0111i\u1ec3m duy nh\u1ea5t; trong tr\u01b0\u1eddng h\u1ee3p song song, kh\u00f4ng c\u00f3 giao \u0111i\u1ec3m.<br \/>\n&#8211; Giao \u0111i\u1ec3m gi\u1eefa c\u00e1c h\u00ecnh h\u1ecdc kh\u00e1c nhau: C\u00e1c h\u00ecnh h\u1ecdc kh\u00e1c nhau nh\u01b0 v\u00f2ng tr\u00f2n v\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng c\u00f3 th\u1ec3 c\u00f3 t\u1eeb 0 \u0111\u1ebfn nhi\u1ec1u giao \u0111i\u1ec3m. S\u1ed1 l\u01b0\u1ee3ng giao \u0111i\u1ec3m ph\u1ee5 thu\u1ed9c v\u00e0o v\u1ecb tr\u00ed v\u00e0 h\u00ecnh d\u1ea1ng c\u1ee7a c\u00e1c \u0111\u1ed1i t\u01b0\u1ee3ng.<\/p>\n<p>D\u01b0\u1edbi \u0111\u00e2y l\u00e0 m\u1ed9t s\u1ed1 v\u00ed d\u1ee5 v\u1ec1 giao \u0111i\u1ec3m:<br \/>\n&#8211; Hai \u0111\u01b0\u1eddng th\u1eb3ng c\u1eaft nhau t\u1ea1i m\u1ed9t \u0111i\u1ec3m duy nh\u1ea5t.<br \/>\n&#8211; M\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng c\u1eaft qua m\u1eb7t ph\u1eb3ng t\u1ea1i m\u1ed9t \u0111i\u1ec3m duy nh\u1ea5t.<br \/>\n&#8211; M\u1ed9t v\u00f2ng tr\u00f2n v\u00e0 m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng c\u00f3 th\u1ec3 kh\u00f4ng c\u00f3 giao \u0111i\u1ec3m n\u1ebfu ch\u00fang kh\u00f4ng c\u1eaft nhau ho\u1eb7c song song.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Dinh_nghia_cua_giao_diem-6\"><\/span>\u0110\u1ecbnh ngh\u0129a c\u1ee7a giao \u0111i\u1ec3m<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Giao \u0111i\u1ec3m l\u00e0 \u0111i\u1ec3m chung c\u1ee7a hai hay nhi\u1ec1u \u0111\u1ed1i t\u01b0\u1ee3ng, h\u00ecnh d\u1ea1ng ho\u1eb7c \u0111\u01b0\u1eddng th\u1eb3ng. Khi hai \u0111\u1ed1i t\u01b0\u1ee3ng c\u1eaft nhau ho\u1eb7c c\u00f3 m\u1ed9t \u0111i\u1ec3m chung, ta g\u1ecdi \u0111i\u1ec3m \u0111\u00f3 l\u00e0 giao \u0111i\u1ec3m. Giao \u0111i\u1ec3m c\u00f3 th\u1ec3 l\u00e0 m\u1ed9t \u0111i\u1ec3m duy nh\u1ea5t ho\u1eb7c c\u00f3 th\u1ec3 l\u00e0 m\u1ed9t t\u1eadp h\u1ee3p c\u00e1c \u0111i\u1ec3m.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"Tinh_chat_cua_giao_diem-6\"><\/span>T\u00ednh ch\u1ea5t c\u1ee7a giao \u0111i\u1ec3m<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>&#8211; Giao \u0111i\u1ec3m gi\u1eefa hai \u0111\u01b0\u1eddng th\u1eb3ng: N\u1ebfu hai \u0111\u01b0\u1eddng th\u1eb3ng kh\u00f4ng song song, ch\u00fang s\u1ebd c\u1eaft nhau t\u1ea1i m\u1ed9t \u0111i\u1ec3m duy nh\u1ea5t. N\u1ebfu hai \u0111\u01b0\u1eddng th\u1eb3ng song song, ch\u00fang kh\u00f4ng c\u00f3 giao \u0111i\u1ec3m.<br \/>\n&#8211; Giao \u0111i\u1ec3m gi\u1eefa hai h\u00ecnh tr\u00f2n: Hai h\u00ecnh tr\u00f2n c\u00f3 th\u1ec3 kh\u00f4ng c\u1eaft nhau (kh\u00f4ng c\u00f3 giao \u0111i\u1ec3m), c\u1eaft nhau t\u1ea1i m\u1ed9t ho\u1eb7c hai \u0111i\u1ec3m (giao \u1edf v\u1ecb tr\u00ed b\u00ean trong) ho\u1eb7c ti\u1ebfp x\u00fac v\u1edbi nhau (giao \u1edf v\u1ecb tr\u00ed b\u00ean ngo\u00e0i).<br \/>\n&#8211; Giao \u0111i\u1ec3m gi\u1eefa c\u00e1c h\u00ecnh d\u1ea1ng kh\u00e1c nhau: C\u00e1c h\u00ecnh d\u1ea1ng kh\u00e1c nhau nh\u01b0 tam gi\u00e1c, t\u1ee9 gi\u00e1c, ng\u0169 gi\u00e1c&#8230; c\u00f3 th\u1ec3 c\u1eaft v\u00e0 c\u00f3 nhi\u1ec1u giao \u0111i\u1ec3m kh\u00e1c nhau. S\u1ed1 l\u01b0\u1ee3ng v\u00e0 v\u1ecb tr\u00ed c\u1ee7a giao \u0111i\u1ec3m ph\u1ee5 thu\u1ed9c v\u00e0o h\u00ecnh d\u1ea1ng v\u00e0 v\u1ecb tr\u00ed c\u1ee7a c\u00e1c \u0111\u1ed1i t\u01b0\u1ee3ng.<\/p>\n<p>D\u01b0\u1edbi \u0111\u00e2y l\u00e0 m\u1ed9t s\u1ed1 v\u00ed d\u1ee5 v\u1ec1 giao \u0111i\u1ec3m:<br \/>\n&#8211; Hai \u0111\u01b0\u1eddng th\u1eb3ng c\u1eaft nhau t\u1ea1i m\u1ed9t \u0111i\u1ec3m duy nh\u1ea5t.<br \/>\n&#8211; Hai h\u00ecnh tr\u00f2n c\u00f3 m\u1ed9t \u0111i\u1ec3m chung n\u1eb1m b\u00ean trong.<br \/>\n&#8211; M\u1ed9t tam gi\u00e1c c\u1eaft qua m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng t\u1ea1i ba \u0111i\u1ec3m giao.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Dinh_nghia_cua_giao_diem-7\"><\/span>\u0110\u1ecbnh ngh\u0129a c\u1ee7a giao \u0111i\u1ec3m<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Giao \u0111i\u1ec3m l\u00e0 \u0111i\u1ec3m ho\u1eb7c v\u1ecb tr\u00ed m\u00e0 hai \u0111\u01b0\u1eddng th\u1eb3ng, \u0111\u01b0\u1eddng cong ho\u1eb7c h\u00ecnh h\u1ecdc kh\u00e1c c\u1eaft nhau. \u0110i\u1ec1u n\u00e0y c\u00f3 ngh\u0129a l\u00e0 t\u1ea1i giao \u0111i\u1ec3m, c\u00e1c \u0111\u1ed1i t\u01b0\u1ee3ng h\u00ecnh h\u1ecdc chia s\u1ebb c\u00f9ng m\u1ed9t v\u1ecb tr\u00ed ho\u1eb7c \u0111i\u1ec3m trong kh\u00f4ng gian. Giao \u0111i\u1ec3m c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh b\u1eb1ng c\u00e1ch gi\u1ea3i ph\u01b0\u01a1ng tr\u00ecnh c\u1ee7a c\u00e1c \u0111\u01b0\u1eddng th\u1eb3ng ho\u1eb7c \u0111\u01b0\u1eddng cong t\u01b0\u01a1ng \u1ee9ng v\u00e0 xem x\u00e9t s\u1ef1 ch\u1ed3ng l\u1ea5n c\u1ee7a ch\u00fang.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"Tinh_chat_cua_giao_diem-7\"><\/span>T\u00ednh ch\u1ea5t c\u1ee7a giao \u0111i\u1ec3m<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>&#8211; M\u1ed9t giao \u0111i\u1ec3m c\u00f3 th\u1ec3 l\u00e0 m\u1ed9t \u0111i\u1ec3m duy nh\u1ea5t ho\u1eb7c m\u1ed9t t\u1eadp h\u1ee3p c\u00e1c \u0111i\u1ec3m.<br \/>\n&#8211; Hai \u0111\u01b0\u1eddng th\u1eb3ng song song kh\u00f4ng bao gi\u1edd c\u1eaft nhau, do \u0111\u00f3 kh\u00f4ng c\u00f3 giao \u0111i\u1ec3m gi\u1eefa ch\u00fang.<br \/>\n&#8211; \u0110\u1ed1i v\u1edbi hai \u0111\u01b0\u1eddng th\u1eb3ng vu\u00f4ng g\u00f3c nhau, giao \u0111i\u1ec3m c\u1ee7a ch\u00fang l\u00e0 m\u1ed9t \u0111i\u1ec3m duy nh\u1ea5t.<br \/>\n&#8211; \u0110\u1ed1i v\u1edbi c\u00e1c \u0111\u01b0\u1eddng cong, c\u00f3 th\u1ec3 c\u00f3 nhi\u1ec1u giao \u0111i\u1ec3m t\u00f9y thu\u1ed9c v\u00e0o lo\u1ea1i v\u00e0 h\u00ecnh d\u1ea1ng c\u1ee7a t\u1eebng \u0111\u01b0\u1eddng cong.<\/p>\n<p>D\u01b0\u1edbi \u0111\u00e2y l\u00e0 danh s\u00e1ch c\u00e1c t\u00ednh ch\u1ea5t quan tr\u1ecdng li\u00ean quan \u0111\u1ebfn giao \u0111i\u1ec3m:<br \/>\n1. Giao \u0111i\u1ec3m c\u1ee7a hai \u0111\u01b0\u1eddng th\u1eb3ng l\u00e0 \u0111i\u1ec3m duy nh\u1ea5t n\u1ebfu ch\u00fang kh\u00f4ng song song.<br \/>\n2. Giao \u0111i\u1ec3m c\u1ee7a hai \u0111\u01b0\u1eddng th\u1eb3ng song song l\u00e0 m\u1ed9t t\u1eadp h\u1ee3p v\u00f4 h\u1ea1n c\u00e1c \u0111i\u1ec3m.<br \/>\n3. Giao \u0111i\u1ec3m c\u1ee7a hai \u0111\u01b0\u1eddng cong c\u00f3 th\u1ec3 l\u00e0 m\u1ed9t ho\u1eb7c nhi\u1ec1u \u0111i\u1ec3m, t\u00f9y thu\u1ed9c v\u00e0o lo\u1ea1i v\u00e0 h\u00ecnh d\u1ea1ng c\u1ee7a t\u1eebng \u0111\u01b0\u1eddng cong.<br \/>\n4. Hai \u0111\u01b0\u1eddng tr\u00f2n c\u00f3 th\u1ec3 c\u00f3 0, 1 ho\u1eb7c 2 giao \u0111i\u1ec3m, t\u00f9y thu\u1ed9c v\u00e0o v\u1ecb tr\u00ed v\u00e0 b\u00e1n k\u00ednh c\u1ee7a ch\u00fang.<br \/>\n5. Giao \u0111i\u1ec3m c\u1ee7a m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng v\u00e0 m\u1ed9t \u0111\u01b0\u1eddng cong c\u00f3 th\u1ec3 l\u00e0 0, 1 ho\u1eb7c nhi\u1ec1u \u0111i\u1ec3m.<\/p>\n<p>T\u00f3m l\u1ea1i, giao \u0111i\u1ec3m l\u00e0 kh\u00e1i ni\u1ec7m quan tr\u1ecdng trong h\u00ecnh h\u1ecdc v\u00e0 \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 x\u00e1c \u0111\u1ecbnh s\u1ef1 c\u1eaft nhau hay ch\u1ed3ng l\u1ea5n gi\u1eefa c\u00e1c h\u00ecnh h\u1ecdc kh\u00e1c nhau. T\u00ednh ch\u1ea5t c\u1ee7a giao \u0111i\u1ec3m ph\u1ee5 thu\u1ed9c v\u00e0o lo\u1ea1i v\u00e0 h\u00ecnh d\u1ea1ng c\u1ee7a c\u00e1c \u0111\u1ed1i t\u01b0\u1ee3ng \u0111\u01b0\u1ee3c xem x\u00e9t.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Dinh_nghia_cua_giao_diem-8\"><\/span>\u0110\u1ecbnh ngh\u0129a c\u1ee7a giao \u0111i\u1ec3m<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Giao \u0111i\u1ec3m l\u00e0 \u0111i\u1ec3m chung c\u1ee7a hai ho\u1eb7c nhi\u1ec1u \u0111\u1ed1i t\u01b0\u1ee3ng, \u0111\u01b0\u1eddng th\u1eb3ng, \u0111\u01b0\u1eddng cong ho\u1eb7c h\u00ecnh h\u1ecdc kh\u00e1c nhau. Khi hai \u0111\u1ed1i t\u01b0\u1ee3ng c\u1eaft nhau ho\u1eb7c giao nhau t\u1ea1i m\u1ed9t \u0111i\u1ec3m duy nh\u1ea5t, ta g\u1ecdi \u0111i\u1ec3m \u0111\u00f3 l\u00e0 giao \u0111i\u1ec3m. Giao \u0111i\u1ec3m c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh trong kh\u00f4ng gian hai chi\u1ec1u (m\u1eb7t ph\u1eb3ng) ho\u1eb7c kh\u00f4ng gian ba chi\u1ec1u (kh\u00f4ng gian 3D).<\/p>\n<h4><span class=\"ez-toc-section\" id=\"Tinh_chat_cua_giao_diem-8\"><\/span>T\u00ednh ch\u1ea5t c\u1ee7a giao \u0111i\u1ec3m<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>&#8211; M\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng c\u00f3 th\u1ec3 c\u1eaft m\u1ed9t \u0111\u01b0\u1eddng cong t\u1ea1i nhi\u1ec1u \u0111i\u1ec3m, v\u00e0 ng\u01b0\u1ee3c l\u1ea1i, m\u1ed9t \u0111\u01b0\u1eddng cong c\u0169ng c\u00f3 th\u1ec3 c\u1eaft nhi\u1ec1u \u0111\u01b0\u1eddng cong kh\u00e1c.<br \/>\n&#8211; N\u1ebfu hai \u0111\u1ed1i t\u01b0\u1ee3ng kh\u00f4ng c\u00f3 \u0111i\u1ec3m chung, ta n\u00f3i ch\u00fang kh\u00f4ng giao nhau.<br \/>\n&#8211; Trong kh\u00f4ng gian 2D, hai \u0111\u01b0\u1eddng th\u1eb3ng song song s\u1ebd kh\u00f4ng bao gi\u1edd c\u1eaft nhau v\u00e0 do \u0111\u00f3 kh\u00f4ng c\u00f3 giao \u0111i\u1ec3m. Tuy nhi\u00ean, trong kh\u00f4ng gian 3D, hai \u0111\u01b0\u1eddng th\u1eb3ng song song c\u00f3 th\u1ec3 c\u1eaft nhau t\u1ea1i m\u1ed9t \u0111i\u1ec3m duy nh\u1ea5t.<br \/>\n&#8211; Hai m\u1eb7t ph\u1eb3ng song song s\u1ebd kh\u00f4ng bao gi\u1edd c\u1eaft nhau v\u00e0 do \u0111\u00f3 kh\u00f4ng c\u00f3 giao \u0111i\u1ec3m.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Dinh_nghia_cua_giao_diem-9\"><\/span>\u0110\u1ecbnh ngh\u0129a c\u1ee7a giao \u0111i\u1ec3m<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Giao \u0111i\u1ec3m l\u00e0 \u0111i\u1ec3m chung c\u1ee7a hai hay nhi\u1ec1u \u0111\u1ed1i t\u01b0\u1ee3ng, v\u1eadt th\u1ec3 ho\u1eb7c h\u1ec7 th\u1ed1ng. Trong to\u00e1n h\u1ecdc, giao \u0111i\u1ec3m th\u01b0\u1eddng \u0111\u01b0\u1ee3c s\u1eed d\u1ee5ng \u0111\u1ec3 ch\u1ec9 c\u00e1c \u0111i\u1ec3m m\u00e0 hai \u0111\u01b0\u1eddng th\u1eb3ng, \u0111\u01b0\u1eddng cong ho\u1eb7c h\u00ecnh vu\u00f4ng c\u00f3 chung. Giao \u0111i\u1ec3m c\u0169ng c\u00f3 th\u1ec3 \u00e1p d\u1ee5ng cho c\u00e1c kh\u00e1i ni\u1ec7m kh\u00e1c nh\u01b0 giao \u0111i\u1ec3m c\u1ee7a c\u00e1c t\u1eadp h\u1ee3p hay giao \u0111i\u1ec3m gi\u1eefa c\u00e1c ph\u1ea7n t\u1eed trong m\u1ed9t t\u1eadp h\u1ee3p.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"Tinh_chat_cua_giao_diem-9\"><\/span>T\u00ednh ch\u1ea5t c\u1ee7a giao \u0111i\u1ec3m<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>&#8211; Giao \u0111i\u1ec3m gi\u1eefa hai \u0111\u01b0\u1eddng th\u1eb3ng song song l\u00e0 m\u1ed9t t\u1eadp r\u1ed7ng, t\u1ee9c kh\u00f4ng c\u00f3 \u0111i\u1ec3m chung.<br \/>\n&#8211; Giao \u0111i\u1ec3m gi\u1eefa hai \u0111\u01b0\u1eddng th\u1eb3ng c\u1eaft nhau l\u00e0 m\u1ed9t \u0111i\u1ec3m duy nh\u1ea5t.<br \/>\n&#8211; Giao \u0111i\u1ec3m gi\u1eefa hai \u0111\u01b0\u1eddng cong c\u00f3 th\u1ec3 l\u00e0 m\u1ed9t ho\u1eb7c nhi\u1ec1u \u0111i\u1ec3m.<br \/>\n&#8211; Giao \u0111i\u1ec3m gi\u1eefa hai h\u00ecnh vu\u00f4ng c\u00f3 th\u1ec3 l\u00e0 m\u1ed9t ho\u1eb7c nhi\u1ec1u c\u1ea1nh, ho\u1eb7c kh\u00f4ng c\u00f3 g\u00ec.<\/p>\n<p>D\u01b0\u1edbi \u0111\u00e2y l\u00e0 v\u00ed d\u1ee5 v\u1ec1 t\u00ednh ch\u1ea5t c\u1ee7a giao \u0111i\u1ec3m:<br \/>\n&#8211; Hai \u0111\u01b0\u1eddng tr\u00f2n A v\u00e0 B c\u00f3 t\u00e2m l\u1ea7n l\u01b0\u1ee3t l\u00e0 O1 v\u00e0 O2. N\u1ebfu kho\u1ea3ng c\u00e1ch gi\u1eefa O1 v\u00e0 O2 l\u1edbn h\u01a1n t\u1ed5ng b\u00e1n k\u00ednh c\u1ee7a hai \u0111\u01b0\u1eddng tr\u00f2n, th\u00ec kh\u00f4ng c\u00f3 \u0111i\u1ec3m chung gi\u1eefa A v\u00e0 B.<br \/>\n&#8211; Hai \u0111\u01b0\u1eddng th\u1eb3ng AB v\u00e0 CD c\u1eaft nhau t\u1ea1i m\u1ed9t \u0111i\u1ec3m E. Khi ta di chuy\u1ec3n \u0111i\u1ec3m E, hai \u0111\u01b0\u1eddng th\u1eb3ng v\u1eabn c\u1eaft nhau t\u1ea1i m\u1ed9t \u0111i\u1ec3m duy nh\u1ea5t.<br \/>\n&#8211; Hai \u0111\u01b0\u1eddng cong parabol c\u00f3 th\u1ec3 c\u1eaft nhau t\u1ea1i hai \u0111i\u1ec3m ho\u1eb7c kh\u00f4ng c\u1eaft nhau t\u00f9y thu\u1ed9c v\u00e0o h\u1ec7 s\u1ed1 c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh parabol.<\/p>\n<p>Nh\u01b0 v\u1eady, giao \u0111i\u1ec3m l\u00e0 m\u1ed9t kh\u00e1i ni\u1ec7m quan tr\u1ecdng trong to\u00e1n h\u1ecdc v\u00e0 \u0111\u01b0\u1ee3c \u00e1p d\u1ee5ng r\u1ed9ng r\u00e3i trong nhi\u1ec1u l\u0129nh v\u1ef1c kh\u00e1c nhau.<\/p>\n<h3><span class=\"ez-toc-section\" id=\"Dinh_nghia_giao_diem\"><\/span>\u0110\u1ecbnh ngh\u0129a giao \u0111i\u1ec3m<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Giao \u0111i\u1ec3m l\u00e0 \u0111i\u1ec3m chung c\u1ee7a hai hay nhi\u1ec1u \u0111\u1ed1i t\u01b0\u1ee3ng, \u0111\u01b0\u1eddng th\u1eb3ng, ho\u1eb7c h\u00ecnh h\u1ecdc kh\u00e1c nhau. Khi hai \u0111\u1ed1i t\u01b0\u1ee3ng c\u1eaft nhau ho\u1eb7c c\u00f3 \u0111i\u1ec3m chung, ta g\u1ecdi \u0111i\u1ec3m \u0111\u00f3 l\u00e0 giao \u0111i\u1ec3m. Giao \u0111i\u1ec3m c\u00f3 th\u1ec3 l\u00e0 m\u1ed9t \u0111i\u1ec3m duy nh\u1ea5t ho\u1eb7c m\u1ed9t t\u1eadp h\u1ee3p c\u00e1c \u0111i\u1ec3m.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"Tinh_chat_cua_giao_diem-10\"><\/span>T\u00ednh ch\u1ea5t c\u1ee7a giao \u0111i\u1ec3m<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>1. T\u00ednh duy nh\u1ea5t: M\u1ed7i c\u1eb7p \u0111\u1ed1i t\u01b0\u1ee3ng ch\u1ec9 c\u00f3 m\u1ed9t giao \u0111i\u1ec3m duy nh\u1ea5t.<br \/>\n2. T\u00ednh ph\u1ee5 thu\u1ed9c: Vi\u1ec7c t\u1ed3n t\u1ea1i hay kh\u00f4ng t\u1ed3n t\u1ea1i giao \u0111i\u1ec3m ph\u1ee5 thu\u1ed9c v\u00e0o t\u00ednh ch\u1ea5t v\u00e0 v\u1ecb tr\u00ed c\u1ee7a c\u00e1c \u0111\u1ed1i t\u01b0\u1ee3ng.<br \/>\n3. T\u00ednh b\u1eaft bu\u1ed9c: Hai \u0111\u01b0\u1eddng th\u1eb3ng kh\u00f4ng song song s\u1ebd lu\u00f4n c\u00f3 m\u1ed9t giao \u0111i\u1ec3m.<br \/>\n4. T\u00ednh x\u00e1c \u0111\u1ecbnh: Giao \u0111i\u1ec3m \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh b\u1edfi c\u00e1c th\u00f4ng s\u1ed1 v\u00e0 t\u00ednh ch\u1ea5t ri\u00eang bi\u1ec7t c\u1ee7a t\u1eebng lo\u1ea1i h\u00ecnh h\u1ecdc.<\/p>\n<p>D\u01b0\u1edbi \u0111\u00e2y l\u00e0 danh s\u00e1ch c\u00e1c v\u00ed d\u1ee5 v\u1ec1 giao \u0111i\u1ec3m:<br \/>\n&#8211; Giao \u0111i\u1ec3m gi\u1eefa hai \u0111\u01b0\u1eddng th\u1eb3ng: \u0110\u01b0\u1eddng th\u1eb3ng AB v\u00e0 CD c\u1eaft nhau t\u1ea1i m\u1ed9t giao \u0111i\u1ec3m E.<br \/>\n&#8211; Giao \u0111i\u1ec3m gi\u1eefa hai m\u1eb7t ph\u1eb3ng: M\u1eb7t ph\u1eb3ng P v\u00e0 m\u1eb7t ph\u1eb3ng Q c\u1eaft nhau t\u1ea1o th\u00e0nh m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng g\u1ecdi l\u00e0 \u0111\u01b0\u1eddng c\u1eaft.<br \/>\n&#8211; Giao \u0111i\u1ec3m gi\u1eefa hai h\u00ecnh tr\u00f2n: Hai h\u00ecnh tr\u00f2n c\u00f3 t\u00e2m A v\u00e0 B, b\u00e1n k\u00ednh r1 v\u00e0 r2, n\u1ebfu kho\u1ea3ng c\u00e1ch gi\u1eefa hai t\u00e2m l\u1edbn h\u01a1n hi\u1ec7u c\u1ee7a hai b\u00e1n k\u00ednh (|AB| &gt; |r1 &#8211; r2|) th\u00ec ch\u00fang c\u00f3 hai \u0111i\u1ec3m giao nhau.<br \/>\n&#8211; Giao \u0111i\u1ec3m gi\u1eefa \u0111\u01b0\u1eddng th\u1eb3ng v\u00e0 m\u1eb7t ph\u1eb3ng: \u0110\u01b0\u1eddng th\u1eb3ng AB c\u1eaft m\u1eb7t ph\u1eb3ng P t\u1ea1i m\u1ed9t \u0111i\u1ec3m C.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Dinh_nghia_va_tinh_chat_cua_giao_diem\"><\/span>\u0110\u1ecbnh ngh\u0129a v\u00e0 t\u00ednh ch\u1ea5t c\u1ee7a giao \u0111i\u1ec3m<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p><img decoding=\"async\" alt=\"\u0110\u1ecbnh ngh\u0129a v\u00e0 t\u00ednh ch\u1ea5t c\u1ee7a giao \u0111i\u1ec3m\" src=\"https:\/\/ungdung.hotronghiencuu.com\/open\/wp-content\/uploads\/2023\/09\/giao_diem_dinh_nghia_thuat_ngu_va_tinh_chat.jpeg\" style=\"text-align: center; clear: both; display: block; margin: 0 auto;\" title=\"\u0110\u1ecbnh ngh\u0129a v\u00e0 t\u00ednh ch\u1ea5t c\u1ee7a giao \u0111i\u1ec3m\"\/><\/p>\n<h3><span class=\"ez-toc-section\" id=\"Dinh_nghia_giao_diem-2\"><\/span>\u0110\u1ecbnh ngh\u0129a giao \u0111i\u1ec3m<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>Giao \u0111i\u1ec3m l\u00e0 \u0111i\u1ec3m ho\u1eb7c t\u1eadp h\u1ee3p c\u00e1c \u0111i\u1ec3m m\u00e0 hai \u0111\u01b0\u1eddng th\u1eb3ng, \u0111\u01b0\u1eddng cong ho\u1eb7c h\u00ecnh h\u1ecdc kh\u00e1c c\u1eaft nhau. Giao \u0111i\u1ec3m c\u00f3 th\u1ec3 l\u00e0 m\u1ed9t \u0111i\u1ec3m duy nh\u1ea5t ho\u1eb7c m\u1ed9t t\u1eadp h\u1ee3p c\u00e1c \u0111i\u1ec3m.<\/p>\n<h4><span class=\"ez-toc-section\" id=\"Tinh_chat_cua_giao_diem-11\"><\/span>T\u00ednh ch\u1ea5t c\u1ee7a giao \u0111i\u1ec3m<span class=\"ez-toc-section-end\"><\/span><\/h4>\n<p>1. Giao \u0111i\u1ec3m gi\u1eefa hai \u0111\u01b0\u1eddng th\u1eb3ng: Hai \u0111\u01b0\u1eddng th\u1eb3ng song song kh\u00f4ng c\u00f3 giao \u0111i\u1ec3m. N\u1ebfu hai \u0111\u01b0\u1eddng th\u1eb3ng c\u1eaft nhau, giao \u0111i\u1ec3m s\u1ebd l\u00e0 m\u1ed9t \u0111i\u1ec3m duy nh\u1ea5t.<br \/>\n2. Giao \u0111i\u1ec3m gi\u1eefa \u0111\u01b0\u1eddng cong v\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng: \u0110i\u1ec1u n\u00e0y ph\u1ee5 thu\u1ed9c v\u00e0o lo\u1ea1i \u0111\u01b0\u1eddng cong v\u00e0 v\u1ecb tr\u00ed c\u1ee7a \u0111\u01b0\u1eddng th\u1eb3ng. M\u1ed9t \u0111\u01b0\u1eddng cong c\u00f3 th\u1ec3 c\u00f3 nhi\u1ec1u giao \u0111i\u1ec3m v\u1edbi m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng, trong khi m\u1ed9t s\u1ed1 kh\u00e1c kh\u00f4ng c\u00f3 giao \u0111i\u1ec3m.<br \/>\n3. Giao \u0111i\u1ec3m gi\u1eefa hai \u0111\u01b0\u1eddng cong: Hai \u0111\u01b0\u1eddng cong c\u00f3 th\u1ec3 c\u00f3 t\u1eeb kh\u00f4ng gian chung cho t\u1edbi nhi\u1ec1u giao \u0111i\u1ec3m. S\u1ed1 l\u01b0\u1ee3ng v\u00e0 t\u00ednh ch\u1ea5t c\u1ee7a c\u00e1c giao \u0111i\u1ec3m n\u00e0y ph\u1ee5 thu\u1ed9c v\u00e0o lo\u1ea1i v\u00e0 h\u00ecnh d\u1ea1ng c\u1ee7a hai \u0111\u01b0\u1eddng cong.<\/p>\n<p>D\u01b0\u1edbi \u0111\u00e2y l\u00e0 danh s\u00e1ch c\u00e1c t\u00ednh ch\u1ea5t quan tr\u1ecdng c\u1ee7a giao \u0111i\u1ec3m:<br \/>\n&#8211; Giao \u0111i\u1ec3m c\u1ee7a hai \u0111\u01b0\u1eddng th\u1eb3ng l\u00e0 m\u1ed9t \u0111i\u1ec3m duy nh\u1ea5t.<br \/>\n&#8211; Giao \u0111i\u1ec3m gi\u1eefa \u0111\u01b0\u1eddng th\u1eb3ng v\u00e0 \u0111\u01b0\u1eddng cong c\u00f3 th\u1ec3 l\u00e0 m\u1ed9t ho\u1eb7c nhi\u1ec1u \u0111i\u1ec3m.<br \/>\n&#8211; Giao \u0111i\u1ec3m gi\u1eefa hai \u0111\u01b0\u1eddng cong c\u00f3 th\u1ec3 kh\u00f4ng t\u1ed3n t\u1ea1i, t\u1ed3n t\u1ea1i m\u1ed9t s\u1ed1 h\u1eefu h\u1ea1n ho\u1eb7c v\u00f4 h\u1ea1n c\u00e1c giao \u0111i\u1ec3m.<br \/>\n&#8211; \u0110\u1ed1i v\u1edbi c\u00e1c h\u00ecnh d\u1ea1ng ph\u1ee9c t\u1ea1p, t\u00ednh ch\u1ea5t c\u1ee7a giao \u0111i\u1ec3m c\u00f3 th\u1ec3 \u0111\u01b0\u1ee3c x\u00e1c \u0111\u1ecbnh b\u1eb1ng ph\u01b0\u01a1ng ph\u00e1p t\u00ednh to\u00e1n ho\u1eb7c s\u1eed d\u1ee5ng c\u00f4ng c\u1ee5 h\u00ecnh h\u1ecdc.<\/p>\n<p>Giao \u0111i\u1ec3m l\u00e0 n\u01a1i c\u00e1c \u0111\u01b0\u1eddng g\u1eb7p nhau v\u00e0 t\u1ea1o th\u00e0nh m\u1ed9t \u0111i\u1ec3m chung. N\u00f3 quan tr\u1ecdng trong vi\u1ec7c \u0111i\u1ec1u h\u01b0\u1edbng, gi\u00fap ng\u01b0\u1eddi d\u00e2n di chuy\u1ec3n thu\u1eadn l\u1ee3i v\u00e0 an to\u00e0n. Giao \u0111i\u1ec3m c\u0169ng c\u00f3 th\u1ec3 mang \u00fd ngh\u0129a v\u1ec1 s\u1ef1 g\u1eb7p g\u1ee1, k\u1ebft n\u1ed1i v\u00e0 trao \u0111\u1ed5i gi\u1eefa c\u00e1c c\u00e1 nh\u00e2n, t\u1ed5 ch\u1ee9c v\u00e0 \u00fd ki\u1ebfn kh\u00e1c nhau. \u0110\u00f3 l\u00e0 m\u1ed9t ph\u1ea7n kh\u00f4ng th\u1ec3 thi\u1ebfu c\u1ee7a cu\u1ed9c s\u1ed1ng h\u00e0ng ng\u00e0y c\u1ee7a ch\u00fang ta.<br \/>\n<iframe loading=\"lazy\" title=\"T\u00ecm giao \u0111i\u1ec3m c\u1ee7a \u0111\u01b0\u1eddng th\u1eb3ng v\u00e0 m\u1eb7t ph\u1eb3ng - To\u00e1n 11- Th\u1ea7y Nguy\u1ec5n Qu\u1ed1c Ch\u00ed\" width=\"790\" height=\"444\" src=\"https:\/\/www.youtube.com\/embed\/mPvSW5ey8ck?feature=oembed\" frameborder=\"0\" allow=\"accelerometer; autoplay; clipboard-write; encrypted-media; gyroscope; picture-in-picture; web-share\" allowfullscreen><\/iframe><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Giao \u0111i\u1ec3m l\u00e0 \u0111i\u1ec3m h\u1ee3p nh\u1ea5t c\u1ee7a hai ho\u1eb7c nhi\u1ec1u \u0111\u01b0\u1eddng, tuy\u1ebfn \u0111\u01b0\u1eddng ho\u1eb7c \u00fd ki\u1ebfn kh\u00e1c nhau. 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