{"common":{"save":0,"post_id":"7596","level":3,"total":10,"point":10,"point_extra":0},"segment":[{"id":"5703","post_id":"7596","mon_id":"1159285","chapter_id":"1159392","question":"<p>Trong không gian v\u1edbi h\u1ec7 t\u1ecda \u0111\u1ed9 Oxyz, cho hai vect\u01a1 <span class=\"math-tex\">$\\overrightarrow{a}=(-2;m-1;3),\\overrightarrow{b}=(1;1;-n)$<\/span>. Tìm m, n \u0111\u1ec3 các vect\u01a1 <span class=\"math-tex\">$\\overrightarrow{a},\\overrightarrow{b}$<\/span> ng\u01b0\u1ee3c h\u01b0\u1edbng.<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$m=1;n=\\dfrac{3}{2}$<\/span>","<strong>B.<\/strong> <span class=\"math-tex\">$m=-1;n=\\dfrac{3}{2}$<\/span>","<strong>C.<\/strong> <span class=\"math-tex\">$m=\\dfrac{3}{2};n=-1$<\/span>","<strong>D.<\/strong> <span class=\"math-tex\">$m=-\\dfrac{3}{2};n=-1$<\/span>"],"correct":"2","level":"3","hint":"<p>\u0110\u1ec3 các vect\u01a1 <span class=\"math-tex\">$\\overrightarrow{a},\\overrightarrow{b}$<\/span> ng\u01b0\u1ee3c h\u01b0\u1edbng thì <span class=\"math-tex\">$\\overrightarrow{a}=k\\overrightarrow{b}$<\/span> v\u1edbi k < 0.<\/p>","answer":"<p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>B.<\/strong> <span class=\"math-tex\">$m=-1;n=\\dfrac{3}{2}$<\/span><\/span><\/p><p>\u0110\u1ec3 các vect\u01a1 <span class=\"math-tex\">$\\overrightarrow{a},\\overrightarrow{b}$<\/span> ng\u01b0\u1ee3c h\u01b0\u1edbng thì <span class=\"math-tex\">$\\overrightarrow{a}=k\\overrightarrow{b}$<\/span> v\u1edbi k < 0.<\/p><p>⇔ <span class=\"math-tex\">$\\begin{cases}-2=k\\\\m-1=k\\\\3=-kn\\end{cases}$<\/span> ⇔ <span class=\"math-tex\">$\\begin{cases}k=-2\\\\m=-1\\\\n=\\dfrac{3}{2}\\end{cases}$<\/span><\/p><p>V\u1eady <span style=\"color:#16a085;\"><span class=\"math-tex\">$m=-1;n=\\dfrac{3}{2}$<\/span><\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-09-08 07:54:24","option_type":"math","len":0},{"id":"5705","post_id":"7596","mon_id":"1159285","chapter_id":"1159392","question":"<p>Trong không gian v\u1edbi h\u1ec7 to\u1ea1 \u0111\u1ed9 Oxyz, cho \u0111i\u1ec3m A(2; 2; 1). Tính \u0111\u1ed9 dài \u0111o\u1ea1n th\u1eb3ng OA.<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$OA=\\sqrt{5}$<\/span>","<strong>B.<\/strong> <span class=\"math-tex\">$OA=5$<\/span>","<strong>C.<\/strong> <span class=\"math-tex\">$OA=3$<\/span>","<strong>D.<\/strong> <span class=\"math-tex\">$OA=9$<\/span>"],"correct":"3","level":"3","hint":"","answer":"<p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>C.<\/strong> <span class=\"math-tex\">$OA=3$<\/span><\/span><\/p><p><span class=\"math-tex\">$OA=\\sqrt{2^2+2^2+1^2}=3$<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-09-08 07:59:21","option_type":"math","len":0},{"id":"5707","post_id":"7596","mon_id":"1159285","chapter_id":"1159392","question":"<p>Trong không gian v\u1edbi h\u1ec7 t\u1ecda \u0111\u1ed9 Oxyz, cho hai \u0111i\u1ec3m A(1; –3; 1), B(3; 0; –2). Tính \u0111\u1ed9 dài AB.<\/p>","options":["<strong>A.<\/strong> 26","<strong>B.<\/strong> 2","<strong>C.<\/strong> <span class=\"math-tex\">$\\sqrt{26}$<\/span>","<strong>D.<\/strong> <span class=\"math-tex\">$\\sqrt{22}$<\/span>"],"correct":"4","level":"3","hint":"","answer":"<p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>D.<\/strong> <span class=\"math-tex\">$\\sqrt{22}$<\/span><\/span><\/p><p><span class=\"math-tex\">$\\overrightarrow{AB}=(2;3;-3)$<\/span> ⇒ <span class=\"math-tex\">$AB=\\sqrt{2^2+3^2+(-3)^2}=\\sqrt{22}$<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-09-08 08:05:25","option_type":"math","len":0}]}
