Chú ý: Để đảm bảo quyền lợi và bảo vệ tài khoản của mình
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HomeLớp 12Toán lớp 12 - Sách Kết nối tri thứcBài 8. Biểu thức toạ độ của các phép toán vectơBài tập trung bình
{"common":{"save":0,"post_id":"7618","level":2,"total":10,"point":10,"point_extra":0},"segment":[{"id":"5664","post_id":"7618","mon_id":"1159285","chapter_id":"1159392","question":"<p>Trong không gian v\u1edbi h\u1ec7 t\u1ecda \u0111\u1ed9 Oxyz, cho các vect\u01a1 <span class=\"math-tex\">$\\overrightarrow{a}=(2;m-1;3)$<\/span>, <span class=\"math-tex\">$\\overrightarrow{b}=(1;3;-2n)$<\/span>. Tìm m, n \u0111\u1ec3 các vect\u01a1 <span class=\"math-tex\">$\\overrightarrow{a},\\overrightarrow{b}$<\/span> cùng h\u01b0\u1edbng.<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$m=7;n=-\\dfrac{3}{4}$<\/span>","<strong>B.<\/strong> <span class=\"math-tex\">$m=4;n=-3$<\/span>","<strong>C.<\/strong> <span class=\"math-tex\">$m=1;n=0$<\/span>","<strong>D.<\/strong> <span class=\"math-tex\">$m=7;n=-\\dfrac{4}{3}$<\/span>"],"correct":"1","level":"2","hint":"","answer":"<p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>A.<\/strong> <span class=\"math-tex\">$m=7;n=-\\dfrac{3}{4}$<\/span>.<\/span><\/p><p><span class=\"math-tex\">$\\overrightarrow{a},\\overrightarrow{b}$<\/span> cùng h\u01b0\u1edbng ⇔ <span class=\"math-tex\">$\\overrightarrow{a}=k.\\overrightarrow{b}$<\/span> (k > 0)<\/p><p>⇔ <span class=\"math-tex\">$\\begin{cases}2=k.1\\\\m-1=3k\\\\3=k.(-2n)\\end{cases}$<\/span> ⇔ <span class=\"math-tex\">$\\begin{cases}k=2\\\\m=7\\\\n=-\\dfrac{3}{4}\\end{cases}$<\/span><\/p><p>V\u1eady <span class=\"math-tex\">$m=7;n=-\\dfrac{3}{4}$<\/span>.<\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-09-05 01:52:53","option_type":"math","len":0},{"id":"5666","post_id":"7618","mon_id":"1159285","chapter_id":"1159392","question":"<p>Trong không gian v\u1edbi h\u1ec7 t\u1ecda \u0111\u1ed9 Oxyz, cho ba \u0111i\u1ec3m <span class=\"math-tex\">$A(2;-1;5),B(5;-5;7),M(x;y;1)$<\/span>. V\u1edbi giá tr\u1ecb nào c\u1ee7a x, y thì A, B, M th\u1eb3ng hàng.<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$x=4;y=7$<\/span>","<strong>B.<\/strong> <span class=\"math-tex\">$x=-4;y=-7$<\/span>","<strong>C.<\/strong> <span class=\"math-tex\">$x=4;y=-7$<\/span>","<strong>D.<\/strong> <span class=\"math-tex\">$x=-4;y=7$<\/span>"],"correct":"4","level":"2","hint":"","answer":"<p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>D.<\/strong> <span class=\"math-tex\">$x=-4;y=7$<\/span>.<\/span><\/p><p><span class=\"math-tex\">$\\overrightarrow{AB}=(3;-4;2)$<\/span>, <span class=\"math-tex\">$\\overrightarrow{AM}=(x-2;y+1;-4)$<\/span><\/p><p>A, B, M th\u1eb3ng hàng ⇔ <span class=\"math-tex\">$\\overrightarrow{AB},\\overrightarrow{AM}$<\/span> cùng ph\u01b0\u01a1ng<\/p><p>⇔ <span class=\"math-tex\">$\\dfrac{x-2}{3}=\\dfrac{y+1}{-4}=\\dfrac{-4}{2}$<\/span> ⇔ <span class=\"math-tex\">$x=-4;y=7$<\/span>.<\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-09-05 01:59:19","option_type":"math","len":0},{"id":"5667","post_id":"7618","mon_id":"1159285","chapter_id":"1159392","question":"<p>Trong không gian Oxyz, cho hai \u0111i\u1ec3m <span class=\"math-tex\">$A(2;-2;1),B(0;1;2)$<\/span>. T\u1ecda \u0111\u1ed9 \u0111i\u1ec3m M thu\u1ed9c m\u1eb7t ph\u1eb3ng Oxy sao cho ba \u0111i\u1ec3m A, B, M th\u1eb3ng hàng là<\/p>","options":["<strong>A.<\/strong> M (4; –5; 0)","<strong>B.<\/strong> M (2; –3; 0)","<strong>C.<\/strong> M (0; 0; 1)","<strong>D.<\/strong> M (4; 5; 0)"],"correct":"1","level":"2","hint":"","answer":"<p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>A.<\/strong> M (4; –5; 0).<\/span><\/p><p>G\u1ecdi M (x; y; 0) ∈ (Oxy).<\/p><p><span class=\"math-tex\">$\\overrightarrow{AB}=(-2;3;1)$<\/span>, <span class=\"math-tex\">$\\overrightarrow{AM}=(x-2;y+2;-1)$<\/span>.<\/p><p>A, B, M th\u1eb3ng hàng ⇔ <span class=\"math-tex\">$\\overrightarrow{AB},\\overrightarrow{AM}$<\/span> cùng ph\u01b0\u01a1ng<\/p><p>⇔ <span class=\"math-tex\">$\\dfrac{x-2}{-2}=\\dfrac{y+2}{3}=\\dfrac{-1}{1}$<\/span> ⇔ <span class=\"math-tex\">$x=4;y=-5$<\/span><\/p><p>V\u1eady M (4; –5; 0).<\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-09-05 02:06:54","option_type":"txt","len":2}]}