C\u00e2u 6:<\/b>\u00a0Trong kh\u00f4ng gian Oxyz, v\u1ecb tr\u00ed t\u01b0\u01a1ng \u0111\u1ed1i c\u1ee7a hai \u0111\u01b0\u1eddng th\u1eb3ng :<\/p>\n
d1<\/sub>: x = 2 + 4t, y = -6t, z = -1-8t v\u00e0<\/p>\n <\/p>\n A. C\u1eaft nhau\u00a0\u00a0\u00a0B. song song\u00a0\u00a0\u00a0C. ch\u00e9o nhau\u00a0\u00a0\u00a0D. tr\u00f9ng nhau<\/p>\n C\u00e2u 7:<\/b>\u00a0Trong kh\u00f4ng gian Oxyz, cho ba \u0111i\u1ec3m A(3;0;0), B(0;3;0), C(0;0;3). Trong nh\u1eefng kh\u1eb3ng \u0111\u1ecbnh d\u01b0\u1edbi \u0111\u00e2y, kh\u1eb3ng \u0111\u1ecbnh n\u00e0o sai?<\/p>\n A. Ph\u01b0\u01a1ng tr\u00ecnh c\u1ee7a m\u1eb7t ph\u1eb3ng (ABC) l\u00e0: x + y + z – 3 = 0<\/p>\n B. H\u00ecnh ch\u00f3p O.ABC l\u00e0 h\u00ecnh ch\u00f3p tam gi\u00e1c \u0111\u1ec1u<\/p>\n C. Ph\u01b0\u01a1ng tr\u00ecnh \u0111\u01b0\u1eddng th\u1eb3ng qua O, vu\u00f4ng g\u00f3c v\u1edbi m\u1eb7t ph\u1eb3ng (ABC) l\u00e0: x = t, y = t, z = t<\/p>\n D. Kho\u1ea3ng c\u00e1ch t\u1eeb O \u0111\u1ebfn m\u1eb7t ph\u1eb3ng ABC b\u1eb1ng 3<\/p>\n C\u00e2u 8:<\/b>\u00a0Trong kh\u00f4ng gian Oxyz, cho \u0111\u01b0\u1eddng th\u1eb3ng \u0394: x = 1 + 2, y = 2 + t, z = 1 + 2t v\u00e0 \u0111i\u1ec3m M(2; 1; 4). Kho\u1ea3ng c\u00e1ch t\u1eeb M \u0111\u1ebfn \u0111\u01b0\u1eddng th\u1eb3ng \u0394 l\u00e0:<\/p>\n A. 5\u00a0\u00a0\u00a0B. \u221a3 \u00a0\u00a0\u00a0C. \u221a5 \u00a0\u00a0\u00a0D. \u0110\u00e1p \u00e1n kh\u00e1c<\/p>\n C\u00e2u 9:<\/b>\u00a0Trong kh\u00f4ng gian Oxyz, cho hai \u0111\u01b0\u1eddng th\u1eb3ng ch\u00e9o nhau :<\/p>\n <\/p>\n Cho m\u1eb7t c\u1ea7u (S) c\u00f3 m\u1ed9t \u0111\u01b0\u1eddng k\u00ednh l\u00e0 \u0111o\u1ea1n vu\u00f4ng g\u00f3c chung c\u1ee7a hai \u0111\u01b0\u1eddng th\u1eb3ng \u0111\u00e3 cho. B\u00e1n k\u00ednh c\u1ee7a m\u1eb7t c\u1ea7u (S) l\u00e0 :<\/p>\n <\/p>\n C\u00e2u 10:<\/b>\u00a0Cho tam gi\u00e1c ABC c\u00f3 ABC c\u00f3 A(2; 2; 1), B(4; 4; 2), C(-2; 4; -3) . Vect\u01a1 n\u00e0o d\u01b0\u1edbi \u0111\u00e2y l\u00e0 vect\u01a1 ch\u1ec9 ph\u01b0\u01a1ng c\u1ee7a \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c trong AD c\u1ee7a tam gi\u00e1c ABC.<\/p>\n \u00a0<\/p>\n H\u01b0\u1edbng d\u1eabn gi\u1ea3i v\u00e0 \u0110\u00e1p \u00e1n<\/b><\/p>\n C\u00e2u 6:<\/b><\/p>\n \u0110\u01b0\u1eddng th\u1eb3ng d1<\/sub>\u00a0\u0111i qua \u0111i\u1ec3m M1<\/sub>(2; 0; -1) v\u00e0 c\u00f3 vect\u01a1 ch\u1ec9 ph\u01b0\u01a1ng l\u00e0\u00a0u1<\/sub>\u2192<\/i>\u00a0= (4; -6; -8) ; \u0111\u01b0\u1eddng th\u1eb3ng d2<\/sub>\u00a0\u0111i qua \u0111i\u1ec3m M2<\/sub>(7; 2; 0) v\u00e0 c\u00f3 vect\u01a1 ch\u1ec9 ph\u01b0\u01a1ng l\u00e0\u00a0u2<\/sub>\u2192<\/i>\u00a0= (-6; 9; 12) . Do hai vect\u01a1\u00a0u1<\/sub>\u2192<\/i>\u00a0v\u00e0\u00a0u2<\/sub>\u2192<\/i>\u00a0c\u00f9ng ph\u01b0\u01a1ng n\u00ean c\u00e1c \u0111\u00e1p \u00e1n A v\u00e0 C l\u00e0 sai. Trong hai \u0111\u00e1p \u00e1n c\u00f2n l\u1ea1i, ta th\u1ea5y :<\/p>\n <\/p>\n Do \u0111\u00f3 hai \u0111\u01b0\u1eddng th\u1eb3ng d1<\/sub>\u00a0v\u00e0 d2<\/sub>\u00a0song song.<\/p>\n V\u1eady \u0111\u00e1p \u00e1n B l\u00e0 \u0111\u00fang<\/p>\n C\u00e2u 7:<\/b><\/p>\n Ph\u01b0\u01a1ng tr\u00ecnh m\u1eb7t ph\u1eb3ng (ABC) l\u00e0:<\/p>\n <\/p>\n T\u1eeb \u0111\u00f3 suy ra kho\u1ea3ng c\u00e1ch t\u1eeb O \u0111\u1ebfn m\u1eb7t ph\u1eb3ng (ABC) l\u00e0:<\/p>\n <\/p>\n V\u1eady kh\u1eb3ng \u0111\u1ecbnh D l\u00e0 kh\u1eb3ng \u0111\u1ecbnh sai.<\/p>\n C\u00e2u 8:<\/b><\/p>\n C\u00e1ch 1. G\u1ecdi H l\u00e0 h\u00ecnh chi\u1ebfu vu\u00f4ng g\u00f3c c\u1ee7a M tr\u00ean \u0111\u01b0\u1eddng th\u1eb3ng \u0394.<\/p>\n Ta c\u00f3: H \u2208 \u0394 => H(1 + t; 2 + t; 1 + 2t)<\/p>\n <\/p>\n <=> 6t – 6 = 0 <=> t = 1 => H(2; 3; 3)<\/p>\n V\u1eady kho\u1ea3ng c\u00e1ch t\u1eeb M \u0111\u1ebfn \u0111\u01b0\u1eddng th\u1eb3ng \u0394 l\u00e0:<\/p>\n <\/p>\n V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 C<\/p>\n C\u00e1ch 2. \u0394 \u0111i qua \u0111i\u1ec3m A(1 ;2 ;1) v\u00e0 c\u00f3 vect\u01a1 ch\u1ec9 ph\u01b0\u01a1ng l\u00e0<\/p>\n <\/p>\n Ta c\u00f3:<\/p>\n <\/p>\n C\u00e2u 9:<\/b><\/p>\n Ta c\u00f3 d1<\/sub>\u00a0\u0111i qua \u0111i\u1ec3m M1<\/sub>(7; 3; 9) v\u00e0 c\u00f3 vect\u01a1 ch\u1ec9 ph\u01b0\u01a1ng l\u00e0\u00a0u1<\/sub>\u2192<\/i>\u00a0= (1; 2; 1); d2<\/sub>\u00a0\u0111i qua \u0111i\u1ec3m M2<\/sub>(3; 1; 1) v\u00e0 c\u00f3 vect\u01a1 ch\u1ec9 ph\u01b0\u01a1ng l\u00e0\u00a0u2<\/sub>\u2192<\/i>\u00a0.<\/p>\n <\/p>\n B\u00e1n k\u00ednh c\u1ee7a m\u1eb7t c\u1ea7u (S) l\u00e0 :<\/p>\n <\/p>\n V\u1eady \u0111\u00e1p \u00e1n \u0111\u00fang l\u00e0 B.<\/p>\n C\u00e2u 10:<\/b><\/p>\n Ta c\u00f3:<\/p>\n <\/p>\n T\u1eeb \u0111i\u1ec3m D k\u1ebb \u0111\u01b0\u1eddng th\u1eb3ng song song v\u1edbi AC, c\u1eaft c\u1ea1nh AB t\u1ea1i \u0111i\u1ec3m E. T\u1eeb D k\u1ebb \u0111\u01b0\u1eddng th\u1eb3ng song song v\u1edbi AB c\u1eaft c\u1ea1nh AC t\u1ea1i F. Do AD l\u00e0 \u0111\u01b0\u1eddng ph\u00e2n gi\u00e1c trong c\u1ee7a tam gi\u00e1c ABC n\u00ean ta suy ra AEDF l\u00e0 h\u00ecnh thoi.<\/p>\n \u0110\u1eb7t AE=AF=k. Ta c\u00f3:<\/p>\n <\/p>\n l\u00e0 m\u1ed9t vect\u01a1 ch\u1ec9 ph\u01b0\u01a1ng c\u1ee7a \u0111\u01b0\u1eddng th\u1eb3ng AD. T\u1eeb \u0111\u00f3 suy ra C l\u00e0 kh\u1eb3ng \u0111\u1ecbnh \u0111\u00fang.<\/p>\n Ta c\u0169ng l\u01b0u \u00fd r\u1eb1ng kh\u1eb3ng \u0111\u1ecbnh A sai, do tam gi\u00e1c ABC kh\u00f4ng c\u00e2n t\u1ea1i \u0111\u1ec9nh A.<\/p>\n <\/p>\n <\/p>\n <\/p>\n","protected":false},"excerpt":{"rendered":" C\u00e2u 6:\u00a0Trong kh\u00f4ng gian Oxyz, v\u1ecb tr\u00ed t\u01b0\u01a1ng \u0111\u1ed1i c\u1ee7a hai \u0111\u01b0\u1eddng th\u1eb3ng : d1: x = 2 + 4t, y = -6t, z = -1-8t v\u00e0 A. C\u1eaft nhau\u00a0\u00a0\u00a0B. song song\u00a0\u00a0\u00a0C. ch\u00e9o nhau\u00a0\u00a0\u00a0D. tr\u00f9ng nhau C\u00e2u 7:\u00a0Trong kh\u00f4ng gian Oxyz, cho ba \u0111i\u1ec3m A(3;0;0), B(0;3;0), C(0;0;3). Trong nh\u1eefng kh\u1eb3ng \u0111\u1ecbnh d\u01b0\u1edbi \u0111\u00e2y, kh\u1eb3ng \u0111\u1ecbnh […]<\/p>\n","protected":false},"author":3,"featured_media":27747,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_mi_skip_tracking":false,"tdm_status":"","tdm_grid_status":""},"categories":[157],"tags":[1450,1448],"yoast_head":"\n\n\n
\n 6-B<\/td>\n 7-D<\/td>\n 8-C<\/td>\n 9-B<\/td>\n 10-C<\/td>\n<\/tr>\n<\/tbody>\n<\/table>\n