{"id":2219,"date":"2026-04-25T02:37:12","date_gmt":"2026-04-25T02:37:12","guid":{"rendered":"https:\/\/77.buffdemo.com\/index.php\/2026\/04\/25\/toan-12-phuong-trinh-mat-phang-duong-thang-mat-cau\/"},"modified":"2026-04-25T02:37:12","modified_gmt":"2026-04-25T02:37:12","slug":"toan-12-phuong-trinh-mat-phang-duong-thang-mat-cau","status":"publish","type":"post","link":"https:\/\/77.buffdemo.com\/index.php\/2026\/04\/25\/toan-12-phuong-trinh-mat-phang-duong-thang-mat-cau\/","title":{"rendered":"To\u00e1n 12 Ch\u01b0\u01a1ng 5: Ph\u01b0\u01a1ng tr\u00ecnh m\u1eb7t ph\u1eb3ng, \u0111\u01b0\u1eddng th\u1eb3ng, m\u1eb7t c\u1ea7u"},"content":{"rendered":"<div class=\"entry-content single-page\">\n<p>Chia s\u1ebb t\u00e0i li\u1ec7u To\u00e1n 12 Ch\u01b0\u01a1ng 5: Ph\u01b0\u01a1ng tr\u00ecnh m\u1eb7t ph\u1eb3ng, \u0111\u01b0\u1eddng th\u1eb3ng, m\u1eb7t c\u1ea7u c\u00f3 l\u1eddi gi\u1ea3i chi ti\u1ebft, b\u00e1m s\u00e1t ch\u01b0\u01a1ng tr\u00ecnh m\u1edbi. B\u1ed9 t\u00e0i li\u1ec7u bao g\u1ed3m b\u00e0i gi\u1ea3ng, b\u00e0i t\u1eadp t\u1ef1 luy\u1ec7n v\u00e0 l\u1eddi gi\u1ea3i chi ti\u1ebft cho c\u00e1c b\u1ea1n d\u1ec5 d\u00e0ng \u00f4n t\u1eadp.<\/p>\n<div class=\"code-block code-block-2\" style=\"margin: 8px auto; text-align: center; display: block; clear: both;\">\n<div> <\/div>\n<\/div>\n<h2 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-17d61e5c4ffd67426c1cfd750e97063e\" id=\"h-n\u1ed9i-dung-tai-li\u1ec7u-ch\u01b0\u01a1ng-ph\u01b0\u01a1ng-trinh-m\u1eb7t-ph\u1eb3ng-d\u01b0\u1eddng-th\u1eb3ng-m\u1eb7t-c\u1ea7u\"><span class=\"ez-toc-section\" id=\"Noi_dung_tai_lieu_Chuong_phuong_trinh_mat_phang_duong_thang_mat_cau\"><\/span>N\u1ed9i dung t\u00e0i li\u1ec7u Ch\u01b0\u01a1ng ph\u01b0\u01a1ng tr\u00ecnh m\u1eb7t ph\u1eb3ng, \u0111\u01b0\u1eddng th\u1eb3ng, m\u1eb7t c\u1ea7u<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>C\u00e1c t\u00e0i li\u1ec7u n\u00e0y g\u1ed3m c\u00e1c ki\u1ebfn th\u1ee9c c\u01a1 b\u1ea3n v\u1ec1\u00a0ph\u01b0\u01a1ng tr\u00ecnh m\u1eb7t ph\u1eb3ng, \u0111\u1ecbnh ngh\u0129a v\u00e0 c\u00e1ch x\u00e1c \u0111\u1ecbnh\u00a0vect\u01a1 ph\u00e1p tuy\u1ebfn\u00a0(s\u1eed d\u1ee5ng t\u00edch c\u00f3 h\u01b0\u1edbng) v\u00e0\u00a0ph\u01b0\u01a1ng tr\u00ecnh t\u1ed5ng qu\u00e1t\u00a0c\u1ee7a m\u1eb7t ph\u1eb3ng. Ngo\u00e0i ra, n\u00f3 c\u00f2n cung c\u1ea5p c\u00f4ng th\u1ee9c v\u00e0 v\u00ed d\u1ee5 minh h\u1ecda chi ti\u1ebft v\u1ec1 c\u00e1ch t\u00ednh\u00a0kho\u1ea3ng c\u00e1ch\u00a0t\u1eeb m\u1ed9t \u0111i\u1ec3m \u0111\u1ebfn m\u1eb7t ph\u1eb3ng, kho\u1ea3ng c\u00e1ch gi\u1eefa hai m\u1eb7t ph\u1eb3ng song song, v\u00e0 c\u00e1ch l\u1eadp\u00a0ph\u01b0\u01a1ng tr\u00ecnh \u0111\u01b0\u1eddng th\u1eb3ng\u00a0v\u00e0\u00a0m\u1eb7t c\u1ea7u\u00a0trong kh\u00f4ng gian.<\/p>\n<p>Nhi\u1ec1u v\u00ed d\u1ee5 v\u00e0 b\u00e0i t\u1eadp th\u1ef1c t\u1ebf \u0111\u01b0\u1ee3c \u0111\u01b0a ra, li\u00ean quan \u0111\u1ebfn c\u00e1c \u1ee9ng d\u1ee5ng nh\u01b0 m\u00f4men l\u1ef1c, thi\u1ebft k\u1ebf \u0111\u1ed3 h\u1ecda 3D, qu\u1ef9 \u0111\u1ea1o b\u00f3ng, v\u00e0 v\u00f9ng ph\u1ee7 s\u00f3ng radar\/thi\u00ean th\u1ea1ch.<\/p>\n<h3 class=\"wp-block-heading\" id=\"h-cac-ch\u1ee7-d\u1ec1-tr\u1ecdng-tam\"><span class=\"ez-toc-section\" id=\"Cac_chu_de_trong_tam\"><\/span><strong>C\u00e1c ch\u1ee7 \u0111\u1ec1 tr\u1ecdng t\u00e2m<\/strong><span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>C\u00e1c ch\u1ee7 \u0111\u1ec1 tr\u1ecdng t\u00e2m xoay quanh vi\u1ec7c x\u00e1c \u0111\u1ecbnh v\u00e0 m\u00f4 t\u1ea3 m\u1eb7t ph\u1eb3ng (B\u00e0i 1), \u0111\u01b0\u1eddng th\u1eb3ng (B\u00e0i 2), v\u00e0 m\u1eb7t c\u1ea7u (B\u00e0i 3) trong kh\u00f4ng gian <em>Oxyz<\/em> b\u1eb1ng ph\u01b0\u01a1ng ph\u00e1p t\u1ecda \u0111\u1ed9.<\/p>\n<p><strong>1. Ph\u01b0\u01a1ng tr\u00ecnh M\u1eb7t ph\u1eb3ng (B\u00e0i 1):<\/strong><\/p>\n<ul class=\"wp-block-list\">\n<li><strong>Vect\u01a1 Ph\u00e1p tuy\u1ebfn v\u00e0 C\u1eb7p Vect\u01a1 Ch\u1ec9 ph\u01b0\u01a1ng:<\/strong> \u0110\u1ecbnh ngh\u0129a v\u00e0 t\u00ednh ch\u1ea5t c\u1ee7a vect\u01a1 ph\u00e1p tuy\u1ebfn (<em>n<\/em><img decoding=\"async\" src=\"\"\/>) v\u00e0 c\u1eb7p vect\u01a1 ch\u1ec9 ph\u01b0\u01a1ng (<em>a<\/em><img decoding=\"async\" src=\"\"\/>,<em>b<\/em><img decoding=\"async\" src=\"\"\/>) c\u1ee7a m\u1eb7t ph\u1eb3ng. M\u1ed1i quan h\u1ec7 gi\u1eefa ch\u00fang (t\u00edch c\u00f3 h\u01b0\u1edbng [<em>a<\/em><img decoding=\"async\" src=\"\"\/>,<em>b<\/em><img decoding=\"async\" src=\"\"\/>] l\u00e0 m\u1ed9t vect\u01a1 ph\u00e1p tuy\u1ebfn).<\/li>\n<li><strong>Ph\u01b0\u01a1ng tr\u00ecnh T\u1ed5ng qu\u00e1t:<\/strong> Kh\u00e1i ni\u1ec7m v\u00e0 nh\u1eadn x\u00e9t v\u1ec1 ph\u01b0\u01a1ng tr\u00ecnh t\u1ed5ng qu\u00e1t c\u1ee7a m\u1eb7t ph\u1eb3ng c\u00f3 d\u1ea1ng <em>Ax<\/em>+<em>By<\/em>+<em>Cz<\/em>+<em>D<\/em>=0, trong \u0111\u00f3 <em>n<\/em><img decoding=\"async\" src=\"\"\/>=(<em>A<\/em>;<em>B<\/em>;<em>C<\/em>) l\u00e0 m\u1ed9t vect\u01a1 ph\u00e1p tuy\u1ebfn.<\/li>\n<li><strong>V\u1ecb tr\u00ed T\u01b0\u01a1ng \u0111\u1ed1i:<\/strong> \u0110i\u1ec1u ki\u1ec7n \u0111\u1ec3 hai m\u1eb7t ph\u1eb3ng song song, tr\u00f9ng nhau, c\u1eaft nhau ho\u1eb7c vu\u00f4ng g\u00f3c, d\u1ef1a tr\u00ean m\u1ed1i quan h\u1ec7 gi\u1eefa c\u00e1c vect\u01a1 ph\u00e1p tuy\u1ebfn v\u00e0 h\u1ec7 s\u1ed1 t\u1ef1 do.<\/li>\n<li><strong>Kho\u1ea3ng c\u00e1ch:<\/strong> C\u00f4ng th\u1ee9c t\u00ednh kho\u1ea3ng c\u00e1ch t\u1eeb m\u1ed9t \u0111i\u1ec3m \u0111\u1ebfn m\u1ed9t m\u1eb7t ph\u1eb3ng, v\u00e0 kho\u1ea3ng c\u00e1ch gi\u1eefa hai m\u1eb7t ph\u1eb3ng song song.<\/li>\n<\/ul>\n<p><strong>2. Ph\u01b0\u01a1ng tr\u00ecnh \u0110\u01b0\u1eddng th\u1eb3ng (B\u00e0i 2):<\/strong><\/p>\n<ul class=\"wp-block-list\">\n<li><strong>Vect\u01a1 Ch\u1ec9 ph\u01b0\u01a1ng:<\/strong> \u0110\u1ecbnh ngh\u0129a v\u00e0 t\u00ednh ch\u1ea5t c\u1ee7a vect\u01a1 ch\u1ec9 ph\u01b0\u01a1ng (<em>a<\/em><img decoding=\"async\" src=\"\"\/>) c\u1ee7a \u0111\u01b0\u1eddng th\u1eb3ng.<\/li>\n<li><strong>Ph\u01b0\u01a1ng tr\u00ecnh Tham s\u1ed1 v\u00e0 Ch\u00ednh t\u1eafc:<\/strong> Thi\u1ebft l\u1eadp ph\u01b0\u01a1ng tr\u00ecnh tham s\u1ed1 v\u00e0 ph\u01b0\u01a1ng tr\u00ecnh ch\u00ednh t\u1eafc c\u1ee7a \u0111\u01b0\u1eddng th\u1eb3ng khi bi\u1ebft m\u1ed9t \u0111i\u1ec3m \u0111i qua v\u00e0 vect\u01a1 ch\u1ec9 ph\u01b0\u01a1ng.<\/li>\n<li><strong>V\u1ecb tr\u00ed T\u01b0\u01a1ng \u0111\u1ed1i:<\/strong> X\u00e1c \u0111\u1ecbnh v\u1ecb tr\u00ed t\u01b0\u01a1ng \u0111\u1ed1i gi\u1eefa hai \u0111\u01b0\u1eddng th\u1eb3ng (song song, tr\u00f9ng nhau, c\u1eaft nhau, ch\u00e9o nhau, ho\u1eb7c vu\u00f4ng g\u00f3c), d\u1ef1a tr\u00ean m\u1ed1i quan h\u1ec7 gi\u1eefa c\u00e1c vect\u01a1 ch\u1ec9 ph\u01b0\u01a1ng v\u00e0 m\u1ed9t vect\u01a1 n\u1ed1i hai \u0111i\u1ec3m tr\u00ean hai \u0111\u01b0\u1eddng th\u1eb3ng.<\/li>\n<li><strong>G\u00f3c:<\/strong> C\u00f4ng th\u1ee9c t\u00ednh g\u00f3c gi\u1eefa hai \u0111\u01b0\u1eddng th\u1eb3ng, g\u00f3c gi\u1eefa \u0111\u01b0\u1eddng th\u1eb3ng v\u00e0 m\u1eb7t ph\u1eb3ng, v\u00e0 g\u00f3c gi\u1eefa hai m\u1eb7t ph\u1eb3ng.<\/li>\n<\/ul>\n<p><strong>3. Ph\u01b0\u01a1ng tr\u00ecnh M\u1eb7t c\u1ea7u (B\u00e0i 3):<\/strong><\/p>\n<ul class=\"wp-block-list\">\n<li><strong>Kh\u00e1i ni\u1ec7m v\u00e0 Ph\u01b0\u01a1ng tr\u00ecnh:<\/strong> Kh\u00e1i ni\u1ec7m m\u1eb7t c\u1ea7u <em>S<\/em>(<em>I<\/em>;<em>R<\/em>) v\u00e0 ph\u01b0\u01a1ng tr\u00ecnh m\u1eb7t c\u1ea7u c\u00f3 t\u00e2m <em>I<\/em>(<em>a<\/em>,<em>b<\/em>,<em>c<\/em>) v\u00e0 b\u00e1n k\u00ednh <em>R<\/em>.<\/li>\n<li><strong>D\u1ea1ng T\u1ed5ng qu\u00e1t:<\/strong> Nh\u1eadn bi\u1ebft v\u00e0 chuy\u1ec3n \u0111\u1ed5i t\u1eeb ph\u01b0\u01a1ng tr\u00ecnh d\u1ea1ng t\u1ed5ng qu\u00e1t <em>x<\/em>2+<em>y<\/em>2+<em>z<\/em>2\u22122<em>ax<\/em>\u22122<em>by<\/em>\u22122<em>cz<\/em>+<em>d<\/em>=0 sang d\u1ea1ng chu\u1ea9n, x\u00e1c \u0111\u1ecbnh t\u00e2m <em>I<\/em>(<em>a<\/em>,<em>b<\/em>,<em>c<\/em>) v\u00e0 b\u00e1n k\u00ednh <em>R<\/em> (v\u1edbi \u0111i\u1ec1u ki\u1ec7n <em>a<\/em>2+<em>b<\/em>2+<em>c<\/em>2\u2212<em>d<\/em>&gt;0).<\/li>\n<li><strong>V\u1ecb tr\u00ed T\u01b0\u01a1ng \u0111\u1ed1i:<\/strong> V\u1ecb tr\u00ed t\u01b0\u01a1ng \u0111\u1ed1i c\u1ee7a m\u1eb7t c\u1ea7u v\u1edbi m\u1eb7t ph\u1eb3ng, \u0111\u01b0\u1eddng th\u1eb3ng, v\u00e0 \u0111i\u1ec3m (c\u1eaft, ti\u1ebfp x\u00fac, n\u1eb1m trong\/ngo\u00e0i), d\u1ef1a tr\u00ean so s\u00e1nh kho\u1ea3ng c\u00e1ch t\u1eeb t\u00e2m \u0111\u1ebfn \u0111\u1ed1i t\u01b0\u1ee3ng v\u1edbi b\u00e1n k\u00ednh <em>R<\/em><\/li>\n<\/ul>\n<p class=\"has-text-align-left\"><strong>Xem tr\u01b0\u1edbc t\u00e0i li\u1ec7u:<\/strong><\/p>\n<figure class=\"wp-block-image aligncenter size-full\"><img loading=\"lazy\" decoding=\"async\" alt=\"To\u00e1n 12 Ph\u01b0\u01a1ng tr\u00ecnh m\u1eb7t ph\u1eb3ng, \u0111\u01b0\u1eddng th\u1eb3ng, m\u1eb7t c\u1ea7u\" class=\"wp-image-8455\" height=\"714\" src=\"https:\/\/77.buffdemo.com\/wp-content\/uploads\/2026\/04\/image-17-1.jpg\" width=\"1181\"\/><\/figure>\n<h3 class=\"wp-block-heading\" id=\"h-cac-d\u1ea1ng-bai-t\u1eadp-ph\u01b0\u01a1ng-trinh-m\u1eb7t-ph\u1eb3ng-d\u01b0\u1eddng-th\u1eb3ng-m\u1eb7t-c\u1ea7u\"><span class=\"ez-toc-section\" id=\"Cac_dang_bai_tap_Phuong_trinh_mat_phang_duong_thang_mat_cau\"><\/span>C\u00e1c d\u1ea1ng b\u00e0i t\u1eadp Ph\u01b0\u01a1ng tr\u00ecnh m\u1eb7t ph\u1eb3ng, \u0111\u01b0\u1eddng th\u1eb3ng, m\u1eb7t c\u1ea7u<span class=\"ez-toc-section-end\"><\/span><\/h3>\n<p>C\u00e1c d\u1ea1ng b\u00e0i t\u1eadp trong t\u00e0i li\u1ec7u \u0111\u01b0\u1ee3c ph\u00e2n lo\u1ea1i r\u00f5 r\u00e0ng, t\u1eadp trung v\u00e0o k\u1ef9 n\u0103ng vi\u1ebft ph\u01b0\u01a1ng tr\u00ecnh v\u00e0 \u1ee9ng d\u1ee5ng h\u00ecnh h\u1ecdc gi\u1ea3i t\u00edch trong kh\u00f4ng gian:<\/p>\n<p><strong>B\u00e0i 1: Ph\u01b0\u01a1ng tr\u00ecnh M\u1eb7t ph\u1eb3ng<\/strong><\/p>\n<ul class=\"wp-block-list\">\n<li><strong>D\u1ea1ng 1:<\/strong> Vi\u1ebft ph\u01b0\u01a1ng tr\u00ecnh m\u1eb7t ph\u1eb3ng khi bi\u1ebft m\u1ed9t \u0111i\u1ec3m thu\u1ed9c m\u1eb7t ph\u1eb3ng v\u00e0 t\u00ecm \u0111\u01b0\u1ee3c m\u1ed9t vect\u01a1 ph\u00e1p tuy\u1ebfn.<\/li>\n<li><strong>D\u1ea1ng 2:<\/strong> Vi\u1ebft ph\u01b0\u01a1ng tr\u00ecnh m\u1eb7t ph\u1eb3ng \u0111i qua m\u1ed9t \u0111i\u1ec3m v\u00e0 c\u00f3 c\u1eb7p vect\u01a1 ch\u1ec9 ph\u01b0\u01a1ng. Tr\u01b0\u1eddng h\u1ee3p \u0111\u1eb7c bi\u1ec7t: Vi\u1ebft ph\u01b0\u01a1ng tr\u00ecnh m\u1eb7t ph\u1eb3ng \u0111i qua ba \u0111i\u1ec3m kh\u00f4ng th\u1eb3ng h\u00e0ng (s\u1eed d\u1ee5ng hai vect\u01a1 t\u1ea1o th\u00e0nh c\u1eb7p vect\u01a1 ch\u1ec9 ph\u01b0\u01a1ng).<\/li>\n<li><strong>D\u1ea1ng 3:<\/strong> V\u1ecb tr\u00ed t\u01b0\u01a1ng \u0111\u1ed1i c\u1ee7a hai m\u1eb7t ph\u1eb3ng (x\u00e9t \u0111i\u1ec1u ki\u1ec7n song song, tr\u00f9ng nhau, c\u1eaft nhau, vu\u00f4ng g\u00f3c).<\/li>\n<li><strong>D\u1ea1ng 4:<\/strong> L\u1eadp ph\u01b0\u01a1ng tr\u00ecnh m\u1eb7t ph\u1eb3ng li\u00ean quan \u0111\u1ebfn kho\u1ea3ng c\u00e1ch (s\u1eed d\u1ee5ng c\u00f4ng th\u1ee9c kho\u1ea3ng c\u00e1ch t\u1eeb \u0111i\u1ec3m \u0111\u1ebfn m\u1eb7t ph\u1eb3ng).<\/li>\n<li><strong>D\u1ea1ng 5:<\/strong> To\u00e1n th\u1ef1c t\u1ebf (\u1ee9ng d\u1ee5ng t\u1ecda \u0111\u1ed9 trong kh\u00f4ng gian v\u00e0o c\u00e1c t\u00ecnh hu\u1ed1ng th\u1ef1c t\u1ebf nh\u01b0 m\u00f4-men l\u1ef1c, b\u1ed1 tr\u00ed ph\u00f2ng, qu\u1ef9 \u0111\u1ea1o bay\u2026).<\/li>\n<\/ul>\n<p><strong>B\u00e0i 2: Ph\u01b0\u01a1ng tr\u00ecnh \u0110\u01b0\u1eddng th\u1eb3ng<\/strong><\/p>\n<ul class=\"wp-block-list\">\n<li><strong>D\u1ea1ng 1:<\/strong> X\u00e1c \u0111\u1ecbnh vect\u01a1 ch\u1ec9 ph\u01b0\u01a1ng c\u1ee7a \u0111\u01b0\u1eddng th\u1eb3ng.<\/li>\n<li><strong>D\u1ea1ng 2:<\/strong> Vi\u1ebft ph\u01b0\u01a1ng tr\u00ecnh \u0111\u01b0\u1eddng th\u1eb3ng khi t\u00ecm \u0111\u01b0\u1ee3c m\u1ed9t vect\u01a1 ch\u1ec9 ph\u01b0\u01a1ng v\u00e0 \u0111i\u1ec3m thu\u1ed9c \u0111\u01b0\u1eddng th\u1eb3ng (bao g\u1ed3m c\u00e1c tr\u01b0\u1eddng h\u1ee3p: \u0111i qua hai \u0111i\u1ec3m, song song v\u1edbi \u0111\u01b0\u1eddng th\u1eb3ng kh\u00e1c, vu\u00f4ng g\u00f3c v\u1edbi m\u1eb7t ph\u1eb3ng, l\u00e0 giao tuy\u1ebfn c\u1ee7a hai m\u1eb7t ph\u1eb3ng).<\/li>\n<li><strong>D\u1ea1ng 3:<\/strong> Vi\u1ebft ph\u01b0\u01a1ng tr\u00ecnh \u0111\u01b0\u1eddng th\u1eb3ng b\u1eb1ng ph\u01b0\u01a1ng ph\u00e1p tham s\u1ed1 h\u00f3a (bao g\u1ed3m c\u00e1c tr\u01b0\u1eddng h\u1ee3p: h\u00ecnh chi\u1ebfu vu\u00f4ng g\u00f3c, c\u1eaft hai \u0111\u01b0\u1eddng th\u1eb3ng kh\u00e1c, \u0111\u01b0\u1eddng vu\u00f4ng g\u00f3c chung).<\/li>\n<li><strong>D\u1ea1ng 4:<\/strong> V\u1ecb tr\u00ed t\u01b0\u01a1ng \u0111\u1ed1i gi\u1eefa hai \u0111\u01b0\u1eddng th\u1eb3ng.<\/li>\n<li><strong>D\u1ea1ng 5:<\/strong> To\u00e1n th\u1ef1c t\u1ebf v\u1ec1 \u0111\u01b0\u1eddng th\u1eb3ng (\u1ee9ng d\u1ee5ng trong h\u00e0ng kh\u00f4ng, \u0111o \u0111\u1ea1c, v\u1eadt l\u00fd).<\/li>\n<li><strong>D\u1ea1ng 7, 8, 9:<\/strong> T\u00ednh g\u00f3c (g\u00f3c gi\u1eefa hai m\u1eb7t ph\u1eb3ng, g\u00f3c gi\u1eefa hai \u0111\u01b0\u1eddng th\u1eb3ng, g\u00f3c gi\u1eefa \u0111\u01b0\u1eddng th\u1eb3ng v\u00e0 m\u1eb7t ph\u1eb3ng).<\/li>\n<li>\u2022 <strong>D\u1ea1ng 10:<\/strong> To\u00e1n th\u1ef1c t\u1ebf v\u1ec1 g\u00f3c (\u1ee9ng d\u1ee5ng trong ki\u1ebfn tr\u00fac, h\u00e0ng h\u1ea3i).<\/li>\n<\/ul>\n<p><strong>B\u00e0i 3: Ph\u01b0\u01a1ng tr\u00ecnh M\u1eb7t c\u1ea7u<\/strong><\/p>\n<ul class=\"wp-block-list\">\n<li><strong>D\u1ea1ng 1:<\/strong> X\u00e1c \u0111\u1ecbnh t\u00e2m v\u00e0 b\u00e1n k\u00ednh m\u1eb7t c\u1ea7u (t\u1eeb ph\u01b0\u01a1ng tr\u00ecnh chu\u1ea9n ho\u1eb7c t\u1ed5ng qu\u00e1t).<\/li>\n<li><strong>D\u1ea1ng 2:<\/strong> Vi\u1ebft ph\u01b0\u01a1ng tr\u00ecnh m\u1eb7t c\u1ea7u (khi bi\u1ebft t\u00e2m v\u00e0 b\u00e1n k\u00ednh, \u0111i qua m\u1ed9t \u0111i\u1ec3m, c\u00f3 \u0111\u01b0\u1eddng k\u00ednh l\u00e0 \u0111o\u1ea1n th\u1eb3ng AB, ho\u1eb7c \u0111i qua b\u1ed1n \u0111i\u1ec3m).<\/li>\n<li><strong>D\u1ea1ng 3:<\/strong> M\u1eb7t c\u1ea7u c\u00f3 t\u00e2m thu\u1ed9c \u0111\u01b0\u1eddng th\u1eb3ng\/m\u1eb7t ph\u1eb3ng (v\u00e0 \u0111i qua c\u00e1c \u0111i\u1ec3m cho tr\u01b0\u1edbc).<\/li>\n<li><strong>D\u1ea1ng 4:<\/strong> M\u1eb7t c\u1ea7u ti\u1ebfp x\u00fac \u0111\u01b0\u1eddng th\u1eb3ng\/m\u1eb7t ph\u1eb3ng (s\u1eed d\u1ee5ng kho\u1ea3ng c\u00e1ch t\u1eeb t\u00e2m \u0111\u1ebfn \u0111\u1ed1i t\u01b0\u1ee3ng).<\/li>\n<li><strong>D\u1ea1ng 5:<\/strong> M\u1eb7t c\u1ea7u c\u1eaft \u0111\u01b0\u1eddng th\u1eb3ng\/m\u1eb7t ph\u1eb3ng (t\u00ednh b\u00e1n k\u00ednh \u0111\u01b0\u1eddng tr\u00f2n giao tuy\u1ebfn).<\/li>\n<li><strong>D\u1ea1ng 6:<\/strong> V\u1ecb tr\u00ed t\u01b0\u01a1ng \u0111\u1ed1i li\u00ean quan m\u1eb7t c\u1ea7u (so s\u00e1nh kho\u1ea3ng c\u00e1ch t\u1eeb t\u00e2m \u0111\u1ebfn \u0111i\u1ec3m\/m\u1eb7t ph\u1eb3ng\/\u0111\u01b0\u1eddng th\u1eb3ng v\u1edbi b\u00e1n k\u00ednh).<\/li>\n<li><strong>D\u1ea1ng 7:<\/strong> B\u00e0i to\u00e1n th\u1ef1c t\u1ebf (\u1ee9ng d\u1ee5ng trong \u0111\u1ecbnh v\u1ecb, theo d\u00f5i, kh\u00ed t\u01b0\u1ee3ng, v.v.)<\/li>\n<\/ul>\n<h2 class=\"wp-block-heading has-vivid-red-color has-text-color has-link-color wp-elements-20e8ef4da235d7f6c0d788e3dda244f0\" id=\"h-t\u1ea3i-tai-li\u1ec7u-toan-12-ch\u01b0\u01a1ng-5-ph\u01b0\u01a1ng-trinh-m\u1eb7t-ph\u1eb3ng-d\u01b0\u1eddng-th\u1eb3ng-m\u1eb7t-c\u1ea7u\"><span class=\"ez-toc-section\" id=\"Tai_tai_lieu_Toan_12_Chuong_5_Phuong_trinh_mat_phang_duong_thang_mat_cau\"><\/span>T\u1ea3i t\u00e0i li\u1ec7u To\u00e1n 12 Ch\u01b0\u01a1ng 5 Ph\u01b0\u01a1ng tr\u00ecnh m\u1eb7t ph\u1eb3ng, \u0111\u01b0\u1eddng th\u1eb3ng, m\u1eb7t c\u1ea7u<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>C\u00e1c b\u1ea1n c\u00f3 th\u1ec3 t\u1ea3i t\u00e0i li\u1ec7u \u00f4n t\u1eadp mi\u1ec5n ph\u00ed \u1edf \u0111\u00e2y nh\u00e9<\/p>\n<div class=\"wp-block-buttons is-content-justification-center is-layout-flex wp-container-core-buttons-is-layout-16018d1d wp-block-buttons-is-layout-flex\">\n<div class=\"wp-block-button\"><a class=\"wp-block-button__link has-white-color has-luminous-vivid-orange-background-color has-text-color has-background has-link-color has-text-align-center wp-element-button\" href=\"https:\/\/drive.google.com\/drive\/folders\/1-O8ESERe3fRT84mJnrAYRUB53URuK5Ju?usp=sharing\" rel=\"noreferrer noopener nofollow\" target=\"_blank\"><strong>T\u1ea2I T\u00c0I LI\u1ec6U (\u0110\u1ec0 + \u0110\u00c1P \u00c1N)<\/strong><\/a><\/div>\n<\/div>\n<p>Tham kh\u1ea3o: <strong><a href=\"https:\/\/tailieuonthi.org\/toan-12-chuong-4-nguyen-ham-tich-phan\/\" rel=\"noreferrer noopener\" target=\"_blank\">To\u00e1n 12 Nguy\u00ean h\u00e0m t\u00edch ph\u00e2n<\/a><\/strong><\/p>\n<\/div>\n","protected":false},"excerpt":{"rendered":"<p>Chia s\u1ebb t\u00e0i li\u1ec7u To\u00e1n 12 Ch\u01b0\u01a1ng 5: Ph\u01b0\u01a1ng tr\u00ecnh m\u1eb7t ph\u1eb3ng, \u0111\u01b0\u1eddng th\u1eb3ng, m\u1eb7t c\u1ea7u c\u00f3 l\u1eddi gi\u1ea3i chi ti\u1ebft, b\u00e1m s\u00e1t ch\u01b0\u01a1ng tr\u00ecnh m\u1edbi. B\u1ed9 t\u00e0i li\u1ec7u bao g\u1ed3m b\u00e0i gi\u1ea3ng, b\u00e0i t\u1eadp t\u1ef1 luy\u1ec7n v\u00e0 l\u1eddi gi\u1ea3i chi ti\u1ebft cho c\u00e1c b\u1ea1n d\u1ec5 d\u00e0ng \u00f4n t\u1eadp. N\u1ed9i dung t\u00e0i li\u1ec7u Ch\u01b0\u01a1ng ph\u01b0\u01a1ng [&#8230;]\n","protected":false},"author":1,"featured_media":2217,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[22,23,26],"tags":[],"class_list":["post-2219","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-tai-lieu-thpt","category-tai-lieu-toan","category-toan-12"],"_links":{"self":[{"href":"https:\/\/77.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/2219","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/77.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/77.buffdemo.com\/index.php\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/77.buffdemo.com\/index.php\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/77.buffdemo.com\/index.php\/wp-json\/wp\/v2\/comments?post=2219"}],"version-history":[{"count":0,"href":"https:\/\/77.buffdemo.com\/index.php\/wp-json\/wp\/v2\/posts\/2219\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/77.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media\/2217"}],"wp:attachment":[{"href":"https:\/\/77.buffdemo.com\/index.php\/wp-json\/wp\/v2\/media?parent=2219"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/77.buffdemo.com\/index.php\/wp-json\/wp\/v2\/categories?post=2219"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/77.buffdemo.com\/index.php\/wp-json\/wp\/v2\/tags?post=2219"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}