{"id":4257,"date":"2020-04-16T20:20:49","date_gmt":"2020-04-16T13:20:49","guid":{"rendered":"https:\/\/bacdau.vn\/?post_type=kb&p=4257"},"modified":"2020-04-21T18:48:42","modified_gmt":"2020-04-21T11:48:42","slug":"tich-vo-huong-tich-co-huong","status":"publish","type":"kb","link":"https:\/\/bacdau.vn\/kb\/tich-vo-huong-tich-co-huong\/","title":{"rendered":"T\u00edch V\u00f4 H\u01b0\u1edbng T\u00edch C\u00f3 H\u01b0\u1edbng"},"content":{"rendered":"

Trong to\u00e1n l\u1edbp 10, ph\u1ea7n c\u00e1c <\/span>c\u00f4ng th\u1ee9c to\u00e1n h\u1ecdc v\u1ec1 Vect\u01a1<\/b> \u0111\u01b0\u1ee3c coi l\u00e0 ph\u1ea7n d\u1ec5 l\u1ea5y \u0111i\u1ec3m nh\u1ea5t. Ch\u1ec9 c\u1ea7n h\u1ecdc thu\u1ed9c l\u00f2ng c\u00e1c kh\u00e1i ni\u1ec7m v\u00e0 \u00e1p d\u1ee5ng tr\u1ef1c ti\u1ebfp c\u00f4ng th\u1ee9c c\u00e1c em \u0111\u00e3 c\u00f3 th\u1ec3 \u1eafm tr\u1ecdn \u0111i\u1ec3m cao trong tay r\u1ed3i.<\/span><\/p>\n

\"\"<\/p>\n

1.C\u00e1c \u0111\u1ecbnh ngh\u0129a to\u00e1n h\u1ecdc v\u1ec1 Vect\u01a1<\/span><\/h2>\n

1.1 \u0110\u1ecbnh ngh\u0129a v\u1ec1 Vect\u01a1<\/span><\/h3>\n

Trong to\u00e1n h\u1ecdc, Vect\u01a1 \u0111\u01b0\u1ee3c coi l\u00e0 m\u1ed9t \u0111o\u1ea1n th\u1eb3ng c\u00f3 h\u01b0\u1edbng. M\u1ed9t vect\u01a1 s\u1ebd c\u00f3 m\u1ed9t \u0111i\u1ec3m cu\u1ed1i v\u00e0 m\u1ed9t \u0111i\u1ec3m \u0111\u1ea7u.\u00a0<\/span><\/p>\n

V\u1edbi m\u1ed9t vect\u01a1 c\u00f3 \u0111i\u1ec3m \u0111\u1ea7u l\u00e0 A v\u00e0 \u0111i\u1ec3m cu\u1ed1i l\u00e0 B th\u00ec s\u1ebd \u0111\u01b0\u1ee3c k\u00fd hi\u1ec7u l\u00e0 \u0111o\u1ea1n th\u1eb3ng AB v\u00e0 \u0111\u00e1nh d\u1ea5u m\u0169i t\u00ean \u1edf ph\u00eda B.<\/span><\/p>\n

\"\"<\/p>\n

1.2 \u0110\u1ecbnh ngh\u0129a c\u00f9ng h\u01b0\u1edbng v\u00e0 c\u00f9ng ph\u01b0\u01a1ng c\u1ee7a c\u00e1c vect\u01a1<\/span><\/h3>\n

Gi\u00e1 c\u1ee7a vect\u01a1 l\u00e0 \u0111\u01b0\u1eddng th\u1eb3ng \u0111i qua c\u1ea3 \u0111i\u1ec3m \u0111\u1ea7u v\u00e0 \u0111i\u1ec3m cu\u1ed1i c\u1ee7a Vect\u01a1 \u0111\u00f3.<\/span><\/p>\n

Trong m\u1eb7t ph\u1eb3ng kh\u00f4ng gian l\u1edbp 10, hai vecto s\u1ebd \u0111\u01b0\u1ee3c coi l\u00e0 c\u00f9ng ph\u01b0\u01a1ng khi gi\u00e1 c\u1ee7a ch\u00fang song song v\u1edbi nhau ho\u1eb7c tr\u00f9ng nhau.<\/span><\/p>\n

V\u1edbi hai vect\u01a1 c\u00f9ng ph\u01b0\u01a1ng v\u1edbi nhau c\u00f3 th\u1ec3 x\u1ea3y ra hai h\u1ec7 qu\u1ea3 \u0111\u00f3 l\u00e0 hai vect\u01a1 c\u00f9ng ph\u01b0\u01a1ng v\u00e0 c\u00f9ng h\u01b0\u1edbng ho\u1eb7c ch\u00fang c\u0169ng c\u00f3 th\u1ec3 c\u00f9ng h\u01b0\u1edbng ho\u1eb7c kh\u00e1c h\u01b0\u1edbng. T\u00f9y theo \u0111i\u1ec3m cu\u1ed1i c\u1ee7a c\u00e1c vect\u01a1 m\u00e0 ta c\u00f3 th\u1ec3 x\u00e1c \u0111\u1ecbnh ch\u00fang l\u00e0 h\u01b0\u1edbng hay kh\u00f4ng.<\/span><\/p>\n

Ti\u1ebfp theo h\u00e3y \u0111\u1ebfn v\u1edbi c\u00e1c <\/span>c\u00f4ng th\u1ee9c to\u00e1n h\u1ecdc v\u1ec1 Vect\u01a1<\/b> n\u00e0o<\/span><\/p>\n

2. C\u00f4ng th\u1ee9c to\u00e1n h\u1ecdc v\u1ec1 Vect\u01a1 trong h\u1ec7 t\u1ecda \u0111\u1ed9 XY.<\/span><\/h2>\n

Trong m\u1eb7t ph\u1eb3ng t\u1ecda \u0111\u1ed9 XY, c\u00e1c <\/span>c\u00f4ng th\u1ee9c to\u00e1n h\u1ecdc v\u1ec1 Vect\u01a1<\/b> s\u1ebd bao g\u1ed3m ph\u00e9p c\u1ed9ng c\u1ee7a hai vect\u01a1, ph\u00e9p tr\u1eeb c\u1ee7a hai vect\u01a1, t\u00edch c\u1ee7a hai vect\u01a1 v\u00e0 t\u00edch c\u1ee7a m\u1ed9t vect\u01a1 v\u1edbi 1 s\u1ed1. H\u00e3y b\u1eaft \u0111\u1ea7u v\u1edbi c\u00f4ng th\u1ee9c c\u1ed9ng hai vect\u01a1.<\/span><\/p>\n

2.1 C\u00f4ng th\u1ee9c c\u1ed9ng hai vect\u01a1<\/span><\/h3>\n

Tr\u00ean m\u1ed9t m\u1eb7t ph\u1eb3ng cho hai vect\u01a1 v v\u00e0 z t\u00f9y \u00fd. N\u1ebfu tr\u00ean a ta l\u1ea5y 1 \u0111i\u1ec3m A v\u00e0 v\u1ebd sao cho AB=v v\u00e0 BC= z th\u00ec vecto AC s\u1ebd \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 t\u1ed5ng c\u1ee7a hai vect\u01a1 v v\u00e0 vect\u01a1 z.\u00a0<\/span><\/p>\n

Ngo\u00e0i ra quy t\u1eafc c\u1ed9ng hai vect\u01a1 c\u00f2n \u0111\u01b0\u1ee3c g\u1ecdi l\u00e0 ph\u00e9p to\u00e1n c\u1ed9ng hai vect\u01a1.<\/span><\/p>\n

H\u1ec7 qu\u1ea3: Quy t\u1eafc h\u00ecnh b\u00ecnh h\u00e0nh<\/span><\/p>\n

\"\"<\/p>\n

Ti\u1ebfp \u0111\u00f3 l\u00e0 t\u00ednh ch\u1ea5t c\u1ee7a ph\u00e9p c\u1ed9ng c\u00e1c vecto. \u0110\u00e2y l\u00e0 m\u1ed9t trong nh\u1eefng t\u00ednh ch\u1ea5t quan tr\u1ecdng m\u00e0 c\u00e1c em ph\u1ea3i nh\u1edb k\u1ef9.<\/span><\/p>\n

\"\"<\/p>\n

2.2 C\u00f4ng th\u1ee9c tr\u1eeb gi\u1eefa c\u00e1c vect\u01a1<\/span><\/h3>\n

Tr\u00ean m\u1eb7t ph\u1eb3ng, n\u1ebfu cho tr\u01b0\u1edbc hai vect\u01a1 v v\u00e0 z th\u00ec ta g\u1ecdi hi\u1ec7u c\u1ee7a hai vect\u01a1 v v\u00e0 z l\u00e0 vecto v+(-z) v\u00e0 k\u00fd hi\u1ec7u l\u00e0 vecto\u00a0 v-z.<\/span><\/p>\n

H\u1ec7 qu\u1ea3 c\u1ee7a ph\u00e9p tr\u1eeb hai vect\u01a1 l\u00e0:<\/span><\/p>\n

\"\"<\/span><\/p>\n

2.3 C\u00f4ng th\u1ee9c t\u00ednh t\u00edch c\u1ee7a m\u1ed9t vecto v\u1edbi m\u1ed9t s\u1ed1<\/span><\/h3>\n

C\u00f4ng th\u1ee9c n\u00e0y s\u1ebd \u0111\u01b0\u1ee3c ph\u00e1t bi\u1ec3u nh\u01b0 sau: Cho m\u1ed9t vect\u01a1 a kh\u00e1c kh\u00f4ng v\u00e0 m\u1ed9t s\u1ed1 k c\u0169ng kh\u00e1c kh\u00f4ng.T\u00edch c\u1ee7a ch\u00fang v\u1edbi nhau c\u0169ng s\u1ebd l\u00e0 m\u1ed9t vect\u01a1 v\u00e0 \u0111\u01b0\u1ee3c k\u00fd hi\u1ec7u l\u00e0 ka.<\/span><\/p>\n

T\u00ednh ch\u1ea5t c\u1ea7n nh\u1edb:<\/span><\/p>\n

\"\"<\/span><\/p>\n

Tr\u00ean \u0111\u00e2y l\u00e0 nh\u1eefng <\/span>c\u00f4ng th\u1ee9c to\u00e1n h\u1ecdc v\u1ec1 vect\u01a1<\/b> m\u00e0 c\u00e1c em b\u1eaft bu\u1ed9c ph\u1ea3i h\u1ecdc thu\u1ed9c l\u00f2ng trong ch\u01b0\u01a1ng tr\u00ecnh l\u1edbp 10 v\u00e0 l\u00e0 n\u1ec1n t\u1ea3ng \u0111\u1ec3 h\u1ecdc h\u00ecnh h\u1ecdc kh\u00f4ng gian l\u1edbp 12. Ch\u00fac c\u00e1c em h\u1ecdc gi\u1ecfi.<\/span><\/p>\n","protected":false},"excerpt":{"rendered":"

Trong to\u00e1n l\u1edbp 10, ph\u1ea7n c\u00e1c c\u00f4ng th\u1ee9c to\u00e1n h\u1ecdc v\u1ec1 Vect\u01a1 \u0111\u01b0\u1ee3c coi l\u00e0 ph\u1ea7n d\u1ec5 l\u1ea5y \u0111i\u1ec3m nh\u1ea5t. Ch\u1ec9 c\u1ea7n h\u1ecdc thu\u1ed9c l\u00f2ng c\u00e1c kh\u00e1i ni\u1ec7m v\u00e0 \u00e1p d\u1ee5ng tr\u1ef1c ti\u1ebfp c\u00f4ng th\u1ee9c c\u00e1c em \u0111\u00e3 c\u00f3 th\u1ec3 \u1eafm tr\u1ecdn \u0111i\u1ec3m cao trong tay r\u1ed3i. 1.C\u00e1c \u0111\u1ecbnh ngh\u0129a to\u00e1n h\u1ecdc v\u1ec1 Vect\u01a1 1.1 […]<\/p>\n","protected":false},"author":1,"featured_media":4768,"comment_status":"open","ping_status":"closed","template":"","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-gradient":""}}},"kbtopic":[764],"kbtag":[766],"_links":{"self":[{"href":"https:\/\/bacdau.vn\/wp-json\/wp\/v2\/kb\/4257"}],"collection":[{"href":"https:\/\/bacdau.vn\/wp-json\/wp\/v2\/kb"}],"about":[{"href":"https:\/\/bacdau.vn\/wp-json\/wp\/v2\/types\/kb"}],"author":[{"embeddable":true,"href":"https:\/\/bacdau.vn\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/bacdau.vn\/wp-json\/wp\/v2\/comments?post=4257"}],"version-history":[{"count":0,"href":"https:\/\/bacdau.vn\/wp-json\/wp\/v2\/kb\/4257\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/bacdau.vn\/wp-json\/wp\/v2\/media\/4768"}],"wp:attachment":[{"href":"https:\/\/bacdau.vn\/wp-json\/wp\/v2\/media?parent=4257"}],"wp:term":[{"taxonomy":"kbtopic","embeddable":true,"href":"https:\/\/bacdau.vn\/wp-json\/wp\/v2\/kbtopic?post=4257"},{"taxonomy":"kbtag","embeddable":true,"href":"https:\/\/bacdau.vn\/wp-json\/wp\/v2\/kbtag?post=4257"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}