{"id":620708,"date":"2026-11-09T09:35:38","date_gmt":"2026-11-09T02:35:38","guid":{"rendered":"https:\/\/hoanghamobile.com\/tin-tuc\/?p=620708"},"modified":"2026-11-09T09:35:38","modified_gmt":"2026-11-09T02:35:38","slug":"vecto-phap-tuyen","status":"publish","type":"post","link":"https:\/\/hoanghamobile.com\/tin-tuc\/vecto-phap-tuyen\/","title":{"rendered":"Vect\u01a1 ph\u00e1p tuy\u1ebfn l\u00e0 g\u00ec? C\u00e1ch t\u00ecm v\u00e0 b\u00e0i t\u1eadp c\u00f3 l\u1eddi gi\u1ea3i"},"content":{"rendered":"<p>Vect\u01a1 ph\u00e1p tuy\u1ebfn c\u1ee7a m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng (ho\u1eb7c m\u1eb7t ph\u1eb3ng) l\u00e0 vect\u01a1 kh\u00e1c vect\u01a1 \u2013 kh\u00f4ng v\u00e0 c\u00f3 gi\u00e1 vu\u00f4ng g\u00f3c v\u1edbi \u0111\u01b0\u1eddng th\u1eb3ng (ho\u1eb7c m\u1eb7t ph\u1eb3ng) \u0111\u00f3. \u0110\u01b0\u1eddng th\u1eb3ng ax + by + c = 0 c\u00f3 vect\u01a1 ph\u00e1p tuy\u1ebfn n\u20d7 = (a; b); m\u1eb7t ph\u1eb3ng Ax + By + Cz + D = 0 c\u00f3 vect\u01a1 ph\u00e1p tuy\u1ebfn n\u20d7 = (A; B; C). B\u00e0i vi\u1ebft gi\u1ea3i th\u00edch \u0111\u1ecbnh ngh\u0129a, c\u00e1ch t\u00ecm vect\u01a1 ph\u00e1p tuy\u1ebfn t\u1eeb ph\u01b0\u01a1ng tr\u00ecnh, t\u1eeb vect\u01a1 ch\u1ec9 ph\u01b0\u01a1ng, t\u1eeb hai \u0111i\u1ec3m v\u00e0 \u1ee9ng d\u1ee5ng \u0111\u1ec3 vi\u1ebft ph\u01b0\u01a1ng tr\u00ecnh, k\u00e8m v\u00ed d\u1ee5 c\u00f3 l\u1eddi gi\u1ea3i.<\/p>\n<h2>Vect\u01a1 ph\u00e1p tuy\u1ebfn l\u00e0 g\u00ec?<\/h2>\n<p>Trong m\u1eb7t ph\u1eb3ng, vect\u01a1 n\u20d7 \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 vect\u01a1 ph\u00e1p tuy\u1ebfn c\u1ee7a \u0111\u01b0\u1eddng th\u1eb3ng \u0394 n\u1ebfu n\u20d7 \u2260 0\u20d7 v\u00e0 gi\u00e1 c\u1ee7a n\u20d7 vu\u00f4ng g\u00f3c v\u1edbi \u0394. Trong kh\u00f4ng gian, vect\u01a1 n\u20d7 \u2260 0\u20d7 c\u00f3 gi\u00e1 vu\u00f4ng g\u00f3c v\u1edbi m\u1eb7t ph\u1eb3ng (P) \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 vect\u01a1 ph\u00e1p tuy\u1ebfn c\u1ee7a (P).<\/p>\n<ul>\n<li>M\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng (m\u1eb7t ph\u1eb3ng) c\u00f3 v\u00f4 s\u1ed1 vect\u01a1 ph\u00e1p tuy\u1ebfn; ch\u00fang c\u00f9ng ph\u01b0\u01a1ng v\u1edbi nhau.<\/li>\n<li>N\u1ebfu n\u20d7 l\u00e0 vect\u01a1 ph\u00e1p tuy\u1ebfn th\u00ec k\u00b7n\u20d7 (k \u2260 0) c\u0169ng l\u00e0 vect\u01a1 ph\u00e1p tuy\u1ebfn.<\/li>\n<li>Vect\u01a1 ph\u00e1p tuy\u1ebfn lu\u00f4n vu\u00f4ng g\u00f3c v\u1edbi vect\u01a1 ch\u1ec9 ph\u01b0\u01a1ng c\u1ee7a \u0111\u01b0\u1eddng th\u1eb3ng.<\/li>\n<\/ul>\n<p><img fetchpriority=\"high\" decoding=\"async\" class=\"size-full wp-image-622293 aligncenter\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/vecto-phap-tuyen-1.jpg\" alt=\"vecto-phap-tuyen-1\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/vecto-phap-tuyen-1.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/vecto-phap-tuyen-1-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/vecto-phap-tuyen-1-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h2>Ph\u00e2n bi\u1ec7t vect\u01a1 ph\u00e1p tuy\u1ebfn v\u00e0 vect\u01a1 ch\u1ec9 ph\u01b0\u01a1ng<\/h2>\n<table>\n<thead>\n<tr>\n<th>Ti\u00eau ch\u00ed<\/th>\n<th>Vect\u01a1 ph\u00e1p tuy\u1ebfn<\/th>\n<th>Vect\u01a1 ch\u1ec9 ph\u01b0\u01a1ng<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>V\u1ecb tr\u00ed so v\u1edbi \u0111\u01b0\u1eddng th\u1eb3ng<\/td>\n<td>Vu\u00f4ng g\u00f3c<\/td>\n<td>Song song ho\u1eb7c tr\u00f9ng<\/td>\n<\/tr>\n<tr>\n<td>K\u00fd hi\u1ec7u th\u01b0\u1eddng d\u00f9ng<\/td>\n<td>n\u20d7<\/td>\n<td>u\u20d7<\/td>\n<\/tr>\n<tr>\n<td>\u0110\u1ecdc t\u1eeb ph\u01b0\u01a1ng tr\u00ecnh<\/td>\n<td>Ph\u01b0\u01a1ng tr\u00ecnh t\u1ed5ng qu\u00e1t ax + by + c = 0 \u21d2 (a; b)<\/td>\n<td>Ph\u01b0\u01a1ng tr\u00ecnh tham s\u1ed1 x = x\u2080 + u\u2081t, y = y\u2080 + u\u2082t \u21d2 (u\u2081; u\u2082)<\/td>\n<\/tr>\n<tr>\n<td>Quan h\u1ec7<\/td>\n<td colspan=\"2\">n\u20d7 \u00b7 u\u20d7 = 0; n\u1ebfu u\u20d7 = (u\u2081; u\u2082) th\u00ec n\u20d7 = (u\u2082; \u2212u\u2081)<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<p>M\u1ed9t m\u1eb9o nh\u1edb: &#8220;\u0111\u1ed5i ch\u1ed7, \u0111\u1ed5i d\u1ea5u m\u1ed9t th\u00e0nh ph\u1ea7n&#8221; \u0111\u1ec3 chuy\u1ec3n t\u1eeb vect\u01a1 ch\u1ec9 ph\u01b0\u01a1ng sang vect\u01a1 ph\u00e1p tuy\u1ebfn v\u00e0 ng\u01b0\u1ee3c l\u1ea1i.<\/p>\n<p><img decoding=\"async\" class=\"size-full wp-image-622300 aligncenter\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/vecto-phap-tuyen-2.jpg\" alt=\"vecto-phap-tuyen-2\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/vecto-phap-tuyen-2.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/vecto-phap-tuyen-2-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/vecto-phap-tuyen-2-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h2>C\u00e1ch t\u00ecm vect\u01a1 ph\u00e1p tuy\u1ebfn c\u1ee7a \u0111\u01b0\u1eddng th\u1eb3ng<\/h2>\n<h3>C\u00e1ch 1: T\u1eeb ph\u01b0\u01a1ng tr\u00ecnh t\u1ed5ng qu\u00e1t<\/h3>\n<p>\u0110\u01b0\u1eddng th\u1eb3ng \u0394: 2x \u2212 y + 3 = 0 c\u00f3 vect\u01a1 ph\u00e1p tuy\u1ebfn n\u20d7 = (2; \u22121). B\u1ea1n c\u0169ng c\u00f3 th\u1ec3 d\u00f9ng (\u22122; 1) ho\u1eb7c (4; \u22122) v\u00ec c\u00f9ng ph\u01b0\u01a1ng.<\/p>\n<h3>C\u00e1ch 2: T\u1eeb vect\u01a1 ch\u1ec9 ph\u01b0\u01a1ng<\/h3>\n<p>\u0110\u01b0\u1eddng th\u1eb3ng d c\u00f3 vect\u01a1 ch\u1ec9 ph\u01b0\u01a1ng u\u20d7 = (1; 2) th\u00ec vect\u01a1 ph\u00e1p tuy\u1ebfn l\u00e0 n\u20d7 = (2; \u22121). Ki\u1ec3m tra: n\u20d7 \u00b7 u\u20d7 = 2\u00b71 + (\u22121)\u00b72 = 0.<\/p>\n<h3>C\u00e1ch 3: T\u1eeb hai \u0111i\u1ec3m thu\u1ed9c \u0111\u01b0\u1eddng th\u1eb3ng<\/h3>\n<p>V\u00ed d\u1ee5: Vi\u1ebft ph\u01b0\u01a1ng tr\u00ecnh \u0111\u01b0\u1eddng th\u1eb3ng \u0111i qua A(1; 2) v\u00e0 B(3; 5).<\/p>\n<ul>\n<li>Vect\u01a1 ch\u1ec9 ph\u01b0\u01a1ng AB\u20d7 = (2; 3) \u21d2 vect\u01a1 ph\u00e1p tuy\u1ebfn n\u20d7 = (3; \u22122).<\/li>\n<li>Ph\u01b0\u01a1ng tr\u00ecnh: 3(x \u2212 1) \u2212 2(y \u2212 2) = 0 \u21d4 3x \u2212 2y + 1 = 0.<\/li>\n<li>Ki\u1ec3m tra v\u1edbi B(3; 5): 3\u00b73 \u2212 2\u00b75 + 1 = 0, \u0111\u00fang.<\/li>\n<\/ul>\n<h3>C\u00e1ch 4: T\u1eeb quan h\u1ec7 vu\u00f4ng g\u00f3c, song song<\/h3>\n<ul>\n<li>\u0394 song song v\u1edbi d: ax + by + c = 0 \u21d2 \u0394 c\u00f3 c\u00f9ng vect\u01a1 ph\u00e1p tuy\u1ebfn (a; b).<\/li>\n<li>\u0394 vu\u00f4ng g\u00f3c v\u1edbi d \u21d2 vect\u01a1 ph\u00e1p tuy\u1ebfn c\u1ee7a d l\u00e0 vect\u01a1 ch\u1ec9 ph\u01b0\u01a1ng c\u1ee7a \u0394.<\/li>\n<\/ul>\n<p>C\u00e1c d\u1ea1ng ph\u01b0\u01a1ng tr\u00ecnh v\u00e0 c\u00e1ch chuy\u1ec3n \u0111\u1ed5i \u0111\u01b0\u1ee3c tr\u00ecnh b\u00e0y chi ti\u1ebft trong b\u00e0i <a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/phuong-trinh-duong-thang\/\">ph\u01b0\u01a1ng tr\u00ecnh \u0111\u01b0\u1eddng th\u1eb3ng<\/a>.<\/p>\n<p><img decoding=\"async\" class=\"size-full wp-image-622295 aligncenter\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/vecto-phap-tuyen-3.jpg\" alt=\"vecto-phap-tuyen-3\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/vecto-phap-tuyen-3.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/vecto-phap-tuyen-3-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/vecto-phap-tuyen-3-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h2>Vect\u01a1 ph\u00e1p tuy\u1ebfn c\u1ee7a m\u1eb7t ph\u1eb3ng trong kh\u00f4ng gian Oxyz<\/h2>\n<h3>T\u1eeb ph\u01b0\u01a1ng tr\u00ecnh m\u1eb7t ph\u1eb3ng<\/h3>\n<p>M\u1eb7t ph\u1eb3ng (P): 2x \u2212 y + 2z \u2212 1 = 0 c\u00f3 vect\u01a1 ph\u00e1p tuy\u1ebfn n\u20d7 = (2; \u22121; 2).<\/p>\n<h3>T\u1eeb hai vect\u01a1 kh\u00f4ng c\u00f9ng ph\u01b0\u01a1ng n\u1eb1m trong m\u1eb7t ph\u1eb3ng<\/h3>\n<p>N\u1ebfu u\u20d7 v\u00e0 v\u20d7 l\u00e0 hai vect\u01a1 kh\u00f4ng c\u00f9ng ph\u01b0\u01a1ng c\u00f3 gi\u00e1 song song ho\u1eb7c n\u1eb1m trong (P), th\u00ec vect\u01a1 ph\u00e1p tuy\u1ebfn c\u1ee7a (P) l\u00e0 t\u00edch c\u00f3 h\u01b0\u1edbng n\u20d7 = [u\u20d7, v\u20d7].<\/p>\n<p>V\u00ed d\u1ee5 1: Vi\u1ebft ph\u01b0\u01a1ng tr\u00ecnh m\u1eb7t ph\u1eb3ng \u0111i qua A(1; 0; 0), B(0; 1; 0), C(0; 0; 1).<\/p>\n<ul>\n<li>AB\u20d7 = (\u22121; 1; 0), AC\u20d7 = (\u22121; 0; 1).<\/li>\n<li>n\u20d7 = [AB\u20d7, AC\u20d7] = (1\u00b71 \u2212 0\u00b70; 0\u00b7(\u22121) \u2212 (\u22121)\u00b71; (\u22121)\u00b70 \u2212 1\u00b7(\u22121)) = (1; 1; 1).<\/li>\n<li>Ph\u01b0\u01a1ng tr\u00ecnh: 1(x \u2212 1) + 1(y \u2212 0) + 1(z \u2212 0) = 0 \u21d4 x + y + z \u2212 1 = 0.<\/li>\n<\/ul>\n<p>V\u00ed d\u1ee5 2: M\u1eb7t ph\u1eb3ng qua M(1; \u22121; 2) v\u00e0 ch\u1ee9a hai vect\u01a1 ch\u1ec9 ph\u01b0\u01a1ng u\u20d7 = (1; 2; 3), v\u20d7 = (2; 0; 1).<\/p>\n<ul>\n<li>n\u20d7 = [u\u20d7, v\u20d7] = (2\u00b71 \u2212 3\u00b70; 3\u00b72 \u2212 1\u00b71; 1\u00b70 \u2212 2\u00b72) = (2; 5; \u22124).<\/li>\n<li>Ph\u01b0\u01a1ng tr\u00ecnh: 2(x \u2212 1) + 5(y + 1) \u2212 4(z \u2212 2) = 0 \u21d4 2x + 5y \u2212 4z + 11 = 0.<\/li>\n<\/ul>\n<p>Xem th\u00eam c\u00e1c d\u1ea1ng l\u1eadp ph\u01b0\u01a1ng tr\u00ecnh trong b\u00e0i <a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/phuong-trinh-mat-phang\/\">ph\u01b0\u01a1ng tr\u00ecnh m\u1eb7t ph\u1eb3ng<\/a>.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-622296 aligncenter\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/vecto-phap-tuyen-4.jpg\" alt=\"vecto-phap-tuyen-4\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/vecto-phap-tuyen-4.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/vecto-phap-tuyen-4-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/vecto-phap-tuyen-4-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h2>\u1ee8ng d\u1ee5ng c\u1ee7a vect\u01a1 ph\u00e1p tuy\u1ebfn<\/h2>\n<ul>\n<li>Vi\u1ebft ph\u01b0\u01a1ng tr\u00ecnh: \u0111\u01b0\u1eddng th\u1eb3ng \u0111i qua M(x\u2080; y\u2080) c\u00f3 vect\u01a1 ph\u00e1p tuy\u1ebfn (a; b) l\u00e0 a(x \u2212 x\u2080) + b(y \u2212 y\u2080) = 0.<\/li>\n<li>T\u00ednh kho\u1ea3ng c\u00e1ch: c\u00f4ng th\u1ee9c <a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/khoang-cach-tu-diem-den-duong-thang\/\">kho\u1ea3ng c\u00e1ch t\u1eeb \u0111i\u1ec3m \u0111\u1ebfn \u0111\u01b0\u1eddng th\u1eb3ng<\/a>, m\u1eb7t ph\u1eb3ng d\u00f9ng \u0111\u1ed9 d\u00e0i vect\u01a1 ph\u00e1p tuy\u1ebfn \u1edf m\u1eabu s\u1ed1, v\u00ed d\u1ee5 |ax\u2080 + by\u2080 + c| \/ \u221a(a\u00b2 + b\u00b2).<\/li>\n<li>T\u00ednh g\u00f3c: g\u00f3c gi\u1eefa hai \u0111\u01b0\u1eddng th\u1eb3ng (ho\u1eb7c hai m\u1eb7t ph\u1eb3ng, xem th\u00eam <a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/goc-nhi-dien\/\">g\u00f3c nh\u1ecb di\u1ec7n<\/a>) t\u00ednh qua g\u00f3c gi\u1eefa hai vect\u01a1 ph\u00e1p tuy\u1ebfn: cos\u03c6 = |n\u20d7\u2081 \u00b7 n\u20d7\u2082| \/ (|n\u20d7\u2081|\u00b7|n\u20d7\u2082|).<\/li>\n<li>X\u00e9t v\u1ecb tr\u00ed t\u01b0\u01a1ng \u0111\u1ed1i: hai \u0111\u01b0\u1eddng th\u1eb3ng song song ho\u1eb7c tr\u00f9ng nhau khi vect\u01a1 ph\u00e1p tuy\u1ebfn c\u00f9ng ph\u01b0\u01a1ng; vu\u00f4ng g\u00f3c khi t\u00edch v\u00f4 h\u01b0\u1edbng hai vect\u01a1 ph\u00e1p tuy\u1ebfn b\u1eb1ng 0.<\/li>\n<li>Ti\u1ebfp tuy\u1ebfn c\u1ee7a \u0111\u1ed3 th\u1ecb: \u0111\u01b0\u1eddng ph\u00e1p tuy\u1ebfn t\u1ea1i m\u1ed9t \u0111i\u1ec3m vu\u00f4ng g\u00f3c v\u1edbi <a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/tiep-tuyen-la-gi\/\">ti\u1ebfp tuy\u1ebfn<\/a> t\u1ea1i \u0111i\u1ec3m \u0111\u00f3.<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-622297 aligncenter\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/vecto-phap-tuyen-5.jpg\" alt=\"vecto-phap-tuyen-5\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/vecto-phap-tuyen-5.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/vecto-phap-tuyen-5-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/vecto-phap-tuyen-5-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h2>B\u00e0i t\u1eadp t\u1ef1 luy\u1ec7n vect\u01a1 ph\u00e1p tuy\u1ebfn<\/h2>\n<table>\n<thead>\n<tr>\n<th>B\u00e0i<\/th>\n<th>\u0110\u1ec1 b\u00e0i<\/th>\n<th>\u0110\u00e1p \u00e1n<\/th>\n<\/tr>\n<\/thead>\n<tbody>\n<tr>\n<td>1<\/td>\n<td>T\u00ecm m\u1ed9t vect\u01a1 ph\u00e1p tuy\u1ebfn c\u1ee7a x + 3y \u2212 2 = 0<\/td>\n<td>(1; 3)<\/td>\n<\/tr>\n<tr>\n<td>2<\/td>\n<td>\u0110\u01b0\u1eddng th\u1eb3ng c\u00f3 vect\u01a1 ch\u1ec9 ph\u01b0\u01a1ng (4; \u22121), t\u00ecm vect\u01a1 ph\u00e1p tuy\u1ebfn<\/td>\n<td>(1; 4)<\/td>\n<\/tr>\n<tr>\n<td>3<\/td>\n<td>Vi\u1ebft ph\u01b0\u01a1ng tr\u00ecnh \u0111\u01b0\u1eddng th\u1eb3ng qua A(1; 2), B(3; 5)<\/td>\n<td>3x \u2212 2y + 1 = 0<\/td>\n<\/tr>\n<tr>\n<td>4<\/td>\n<td>T\u00ecm vect\u01a1 ph\u00e1p tuy\u1ebfn c\u1ee7a m\u1eb7t ph\u1eb3ng x \u2212 2y + 5z = 0<\/td>\n<td>(1; \u22122; 5)<\/td>\n<\/tr>\n<tr>\n<td>5<\/td>\n<td>M\u1eb7t ph\u1eb3ng qua A(1; 0; 0), B(0; 1; 0), C(0; 0; 1)<\/td>\n<td>x + y + z \u2212 1 = 0<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n<h2>L\u1ed7i th\u01b0\u1eddng g\u1eb7p khi t\u00ecm vect\u01a1 ph\u00e1p tuy\u1ebfn<\/h2>\n<ul>\n<li>Nh\u1ea7m v\u1edbi vect\u01a1 ch\u1ec9 ph\u01b0\u01a1ng: \u0111\u1ecdc (u\u2081; u\u2082) t\u1eeb ph\u01b0\u01a1ng tr\u00ecnh tham s\u1ed1 r\u1ed3i d\u00f9ng nh\u01b0 vect\u01a1 ph\u00e1p tuy\u1ebfn.<\/li>\n<li>Qu\u00ean \u0111\u1ed5i d\u1ea5u: t\u1eeb u\u20d7 = (1; 2) suy ra n\u20d7 = (2; 1) l\u00e0 sai, ph\u1ea3i l\u00e0 (2; \u22121).<\/li>\n<li>L\u1ea5y c\u1ea3 h\u1ec7 s\u1ed1 t\u1ef1 do: v\u1edbi ax + by + c = 0, vect\u01a1 ph\u00e1p tuy\u1ebfn ch\u1ec9 g\u1ed3m (a; b), kh\u00f4ng c\u00f3 c.<\/li>\n<li>T\u00ednh sai t\u00edch c\u00f3 h\u01b0\u1edbng: n\u00ean vi\u1ebft r\u00f5 t\u1eebng th\u00e0nh ph\u1ea7n v\u00e0 ki\u1ec3m tra l\u1ea1i b\u1eb1ng t\u00edch v\u00f4 h\u01b0\u1edbng v\u1edbi u\u20d7, v\u20d7 (ph\u1ea3i b\u1eb1ng 0).<\/li>\n<\/ul>\n<p><img loading=\"lazy\" decoding=\"async\" class=\"size-full wp-image-622298 aligncenter\" src=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/vecto-phap-tuyen-6.jpg\" alt=\"vecto-phap-tuyen-6\" width=\"800\" height=\"450\" srcset=\"https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/vecto-phap-tuyen-6.jpg 800w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/vecto-phap-tuyen-6-300x169.jpg 300w, https:\/\/hoanghamobile.com\/tin-tuc\/wp-content\/uploads\/2026\/11\/vecto-phap-tuyen-6-768x432.jpg 768w\" sizes=\"(max-width: 800px) 100vw, 800px\" \/><\/p>\n<h2>C\u00e2u h\u1ecfi th\u01b0\u1eddng g\u1eb7p v\u1ec1 vect\u01a1 ph\u00e1p tuy\u1ebfn<\/h2>\n<h3>Vect\u01a1 ph\u00e1p tuy\u1ebfn l\u00e0 g\u00ec?<\/h3>\n<p>Vect\u01a1 ph\u00e1p tuy\u1ebfn c\u1ee7a \u0111\u01b0\u1eddng th\u1eb3ng ho\u1eb7c m\u1eb7t ph\u1eb3ng l\u00e0 vect\u01a1 kh\u00e1c vect\u01a1 \u2013 kh\u00f4ng c\u00f3 gi\u00e1 vu\u00f4ng g\u00f3c v\u1edbi \u0111\u01b0\u1eddng th\u1eb3ng ho\u1eb7c m\u1eb7t ph\u1eb3ng \u0111\u00f3.<\/p>\n<h3>\u0110\u01b0\u1eddng th\u1eb3ng 3x \u2212 4y + 5 = 0 c\u00f3 vect\u01a1 ph\u00e1p tuy\u1ebfn l\u00e0 g\u00ec?<\/h3>\n<p>\u0110\u01b0\u1eddng th\u1eb3ng 3x \u2212 4y + 5 = 0 c\u00f3 vect\u01a1 ph\u00e1p tuy\u1ebfn n\u20d7 = (3; \u22124), ho\u1eb7c b\u1ea5t k\u1ef3 vect\u01a1 n\u00e0o c\u00f9ng ph\u01b0\u01a1ng nh\u01b0 (\u22123; 4), (6; \u22128).<\/p>\n<h3>L\u00e0m sao chuy\u1ec3n t\u1eeb vect\u01a1 ch\u1ec9 ph\u01b0\u01a1ng sang vect\u01a1 ph\u00e1p tuy\u1ebfn?<\/h3>\n<p>V\u1edbi u\u20d7 = (u\u2081; u\u2082), \u0111\u1ed5i ch\u1ed7 hai th\u00e0nh ph\u1ea7n v\u00e0 \u0111\u1ed5i d\u1ea5u m\u1ed9t th\u00e0nh ph\u1ea7n: n\u20d7 = (u\u2082; \u2212u\u2081) ho\u1eb7c (\u2212u\u2082; u\u2081).<\/p>\n<h3>M\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng c\u00f3 bao nhi\u00eau vect\u01a1 ph\u00e1p tuy\u1ebfn?<\/h3>\n<p>C\u00f3 v\u00f4 s\u1ed1 vect\u01a1 ph\u00e1p tuy\u1ebfn, t\u1ea5t c\u1ea3 \u0111\u1ec1u c\u00f9ng ph\u01b0\u01a1ng v\u1edbi nhau v\u00e0 kh\u00e1c vect\u01a1 \u2013 kh\u00f4ng.<\/p>\n<h3>Vect\u01a1 ph\u00e1p tuy\u1ebfn c\u1ee7a m\u1eb7t ph\u1eb3ng t\u00ecm th\u1ebf n\u00e0o?<\/h3>\n<p>\u0110\u1ecdc tr\u1ef1c ti\u1ebfp (A; B; C) t\u1eeb ph\u01b0\u01a1ng tr\u00ecnh Ax + By + Cz + D = 0, ho\u1eb7c l\u1ea5y t\u00edch c\u00f3 h\u01b0\u1edbng c\u1ee7a hai vect\u01a1 kh\u00f4ng c\u00f9ng ph\u01b0\u01a1ng n\u1eb1m trong m\u1eb7t ph\u1eb3ng.<\/p>\n<h3>Vect\u01a1 ph\u00e1p tuy\u1ebfn h\u1ecdc \u1edf l\u1edbp m\u1ea5y?<\/h3>\n<p>Vect\u01a1 ph\u00e1p tuy\u1ebfn c\u1ee7a \u0111\u01b0\u1eddng th\u1eb3ng \u0111\u01b0\u1ee3c h\u1ecdc \u1edf To\u00e1n l\u1edbp 10; vect\u01a1 ph\u00e1p tuy\u1ebfn c\u1ee7a m\u1eb7t ph\u1eb3ng trong kh\u00f4ng gian Oxyz \u0111\u01b0\u1ee3c h\u1ecdc \u1edf To\u00e1n l\u1edbp 12.<\/p>\n<h2>K\u1ebft lu\u1eadn<\/h2>\n<p>Vect\u01a1 ph\u00e1p tuy\u1ebfn l\u00e0 vect\u01a1 vu\u00f4ng g\u00f3c v\u1edbi \u0111\u01b0\u1eddng th\u1eb3ng ho\u1eb7c m\u1eb7t ph\u1eb3ng, \u0111\u1ecdc tr\u1ef1c ti\u1ebfp t\u1eeb h\u1ec7 s\u1ed1 c\u1ee7a ph\u01b0\u01a1ng tr\u00ecnh t\u1ed5ng qu\u00e1t: (a; b) trong m\u1eb7t ph\u1eb3ng v\u00e0 (A; B; C) trong kh\u00f4ng gian. Khi ch\u1ec9 bi\u1ebft vect\u01a1 ch\u1ec9 ph\u01b0\u01a1ng, h\u00e3y \u0111\u1ed5i ch\u1ed7 v\u00e0 \u0111\u1ed5i d\u1ea5u m\u1ed9t th\u00e0nh ph\u1ea7n; khi bi\u1ebft hai vect\u01a1 trong m\u1eb7t ph\u1eb3ng, d\u00f9ng t\u00edch c\u00f3 h\u01b0\u1edbng. N\u1eafm ch\u1eafc vect\u01a1 ph\u00e1p tuy\u1ebfn l\u00e0 n\u1ec1n t\u1ea3ng \u0111\u1ec3 vi\u1ebft ph\u01b0\u01a1ng tr\u00ecnh, t\u00ednh kho\u1ea3ng c\u00e1ch v\u00e0 t\u00ednh g\u00f3c.<\/p>\n<p><strong>Xem th\u00eam:<\/strong><\/p>\n<ul>\n<li><a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/phuong-trinh-duong-thang\/\">Ph\u01b0\u01a1ng tr\u00ecnh \u0111\u01b0\u1eddng th\u1eb3ng: c\u00e1c d\u1ea1ng, h\u1ec7 s\u1ed1 g\u00f3c v\u00e0 v\u00ed d\u1ee5<\/a><\/li>\n<li><a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/phuong-trinh-mat-phang\/\">Ph\u01b0\u01a1ng tr\u00ecnh m\u1eb7t ph\u1eb3ng: c\u00f4ng th\u1ee9c, c\u00e1ch vi\u1ebft v\u00e0 v\u00ed d\u1ee5<\/a><\/li>\n<li><a href=\"https:\/\/hoanghamobile.com\/tin-tuc\/khoang-cach-tu-diem-den-duong-thang\/\">Kho\u1ea3ng c\u00e1ch t\u1eeb \u0111i\u1ec3m \u0111\u1ebfn \u0111\u01b0\u1eddng th\u1eb3ng: c\u00f4ng th\u1ee9c v\u00e0 v\u00ed d\u1ee5<\/a><\/li>\n<\/ul>\n<p><script type=\"application\/ld+json\">{\"@context\": \"https:\/\/schema.org\", \"@type\": \"FAQPage\", \"mainEntity\": [{\"@type\": \"Question\", \"name\": \"Vect\u01a1 ph\u00e1p tuy\u1ebfn l\u00e0 g\u00ec?\", \"acceptedAnswer\": {\"@type\": \"Answer\", \"text\": \"Vect\u01a1 ph\u00e1p tuy\u1ebfn c\u1ee7a \u0111\u01b0\u1eddng th\u1eb3ng ho\u1eb7c m\u1eb7t ph\u1eb3ng l\u00e0 vect\u01a1 kh\u00e1c vect\u01a1 \u2013 kh\u00f4ng c\u00f3 gi\u00e1 vu\u00f4ng g\u00f3c v\u1edbi \u0111\u01b0\u1eddng th\u1eb3ng ho\u1eb7c m\u1eb7t ph\u1eb3ng \u0111\u00f3.\"}}, {\"@type\": \"Question\", \"name\": \"\u0110\u01b0\u1eddng th\u1eb3ng 3x \u2212 4y + 5 = 0 c\u00f3 vect\u01a1 ph\u00e1p tuy\u1ebfn l\u00e0 g\u00ec?\", \"acceptedAnswer\": {\"@type\": \"Answer\", \"text\": \"\u0110\u01b0\u1eddng th\u1eb3ng 3x \u2212 4y + 5 = 0 c\u00f3 vect\u01a1 ph\u00e1p tuy\u1ebfn n\u20d7 = (3; \u22124), ho\u1eb7c b\u1ea5t k\u1ef3 vect\u01a1 n\u00e0o c\u00f9ng ph\u01b0\u01a1ng nh\u01b0 (\u22123; 4), (6; \u22128).\"}}, {\"@type\": \"Question\", \"name\": \"L\u00e0m sao chuy\u1ec3n t\u1eeb vect\u01a1 ch\u1ec9 ph\u01b0\u01a1ng sang vect\u01a1 ph\u00e1p tuy\u1ebfn?\", \"acceptedAnswer\": {\"@type\": \"Answer\", \"text\": \"V\u1edbi u\u20d7 = (u\u2081; u\u2082), \u0111\u1ed5i ch\u1ed7 hai th\u00e0nh ph\u1ea7n v\u00e0 \u0111\u1ed5i d\u1ea5u m\u1ed9t th\u00e0nh ph\u1ea7n: n\u20d7 = (u\u2082; \u2212u\u2081) ho\u1eb7c (\u2212u\u2082; u\u2081).\"}}, {\"@type\": \"Question\", \"name\": \"M\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng c\u00f3 bao nhi\u00eau vect\u01a1 ph\u00e1p tuy\u1ebfn?\", \"acceptedAnswer\": {\"@type\": \"Answer\", \"text\": \"C\u00f3 v\u00f4 s\u1ed1 vect\u01a1 ph\u00e1p tuy\u1ebfn, t\u1ea5t c\u1ea3 \u0111\u1ec1u c\u00f9ng ph\u01b0\u01a1ng v\u1edbi nhau v\u00e0 kh\u00e1c vect\u01a1 \u2013 kh\u00f4ng.\"}}, {\"@type\": \"Question\", \"name\": \"Vect\u01a1 ph\u00e1p tuy\u1ebfn c\u1ee7a m\u1eb7t ph\u1eb3ng t\u00ecm th\u1ebf n\u00e0o?\", \"acceptedAnswer\": {\"@type\": \"Answer\", \"text\": \"\u0110\u1ecdc tr\u1ef1c ti\u1ebfp (A; B; C) t\u1eeb ph\u01b0\u01a1ng tr\u00ecnh Ax + By + Cz + D = 0, ho\u1eb7c l\u1ea5y t\u00edch c\u00f3 h\u01b0\u1edbng c\u1ee7a hai vect\u01a1 kh\u00f4ng c\u00f9ng ph\u01b0\u01a1ng n\u1eb1m trong m\u1eb7t ph\u1eb3ng.\"}}, {\"@type\": \"Question\", \"name\": \"Vect\u01a1 ph\u00e1p tuy\u1ebfn h\u1ecdc \u1edf l\u1edbp m\u1ea5y?\", \"acceptedAnswer\": {\"@type\": \"Answer\", \"text\": \"Vect\u01a1 ph\u00e1p tuy\u1ebfn c\u1ee7a \u0111\u01b0\u1eddng th\u1eb3ng \u0111\u01b0\u1ee3c h\u1ecdc \u1edf To\u00e1n l\u1edbp 10; vect\u01a1 ph\u00e1p tuy\u1ebfn c\u1ee7a m\u1eb7t ph\u1eb3ng trong kh\u00f4ng gian Oxyz \u0111\u01b0\u1ee3c h\u1ecdc \u1edf To\u00e1n l\u1edbp 12.\"}}]}<\/script><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Vect\u01a1 ph\u00e1p tuy\u1ebfn c\u1ee7a m\u1ed9t \u0111\u01b0\u1eddng th\u1eb3ng (ho\u1eb7c m\u1eb7t ph\u1eb3ng) l\u00e0 vect\u01a1 kh\u00e1c vect\u01a1 \u2013 kh\u00f4ng v\u00e0 c\u00f3 gi\u00e1 vu\u00f4ng g\u00f3c v\u1edbi \u0111\u01b0\u1eddng th\u1eb3ng (ho\u1eb7c m\u1eb7t ph\u1eb3ng) \u0111\u00f3. \u0110\u01b0\u1eddng th\u1eb3ng ax + by + c = 0 c\u00f3 vect\u01a1 ph\u00e1p tuy\u1ebfn n\u20d7 = (a; b); m\u1eb7t ph\u1eb3ng Ax + By + Cz + D = [&hellip;]<\/p>\n","protected":false},"author":65,"featured_media":622292,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"vect\u01a1 ph\u00e1p tuy\u1ebfn","_yoast_wpseo_title":"Vect\u01a1 ph\u00e1p tuy\u1ebfn l\u00e0 g\u00ec? C\u00e1ch t\u00ecm c\u1ee7a \u0111\u01b0\u1eddng th\u1eb3ng, m\u1eb7t ph\u1eb3ng","_yoast_wpseo_metadesc":"Vect\u01a1 ph\u00e1p tuy\u1ebfn l\u00e0 vect\u01a1 vu\u00f4ng g\u00f3c v\u1edbi \u0111\u01b0\u1eddng th\u1eb3ng ho\u1eb7c m\u1eb7t ph\u1eb3ng. Xem c\u00e1ch t\u00ecm t\u1eeb ph\u01b0\u01a1ng tr\u00ecnh, vect\u01a1 ch\u1ec9 ph\u01b0\u01a1ng, hai \u0111i\u1ec3m k\u00e8m v\u00ed d\u1ee5 c\u00f3 l\u1eddi gi\u1ea3i.","footnotes":""},"categories":[29235,3910,30453],"tags":[],"class_list":["post-620708","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-goc-to-mo","category-kham-pha","category-kien-thuc"],"yoast_head":"<!-- This site is optimized with the Yoast SEO Premium plugin v27.3 (Yoast SEO v27.4) - https:\/\/yoast.com\/product\/yoast-seo-premium-wordpress\/ -->\n<title>Vect\u01a1 ph\u00e1p tuy\u1ebfn l\u00e0 g\u00ec? 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