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HomeLớp 12Toán lớp 12 - Sách Kết nối tri thứcBài 15. Phương trình đường thẳng trong không gianBài tập cơ bản
{"common":{"save":0,"post_id":"8273","level":1,"total":10,"point":10,"point_extra":0},"segment":[{"id":"6082","post_id":"8273","mon_id":"1159285","chapter_id":"1159382","question":"<p>Trong không gian Oxyz, cho \u0111\u01b0\u1eddng th\u1eb3ng <span class=\"math-tex\">$d:\\begin{cases}x=2+t\\\\y=1-2t\\\\z=-1+3t\\end{cases}$<\/span>. Vect\u01a1 nào d\u01b0\u1edbi \u0111ây là m\u1ed9t vect\u01a1 ch\u1ec9 ph\u01b0\u01a1ng c\u1ee7a d ?<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$\\overrightarrow{u_1}=(2;1;-1)$<\/span>","<strong>B.<\/strong> <span class=\"math-tex\">$\\overrightarrow{u_2}=(1;2;3)$<\/span>","<strong>C.<\/strong> <span class=\"math-tex\">$\\overrightarrow{u_3}=(1;-2;3)$<\/span>","<strong>D.<\/strong> <span class=\"math-tex\">$\\overrightarrow{u_4}=(2;1;1)$<\/span>"],"correct":"3","level":"1","hint":"<p>Trong không gian v\u1edbi h\u1ec7 tr\u1ee5c t\u1ecda \u0111\u1ed9 Oxyz, ph\u01b0\u01a1ng trình tham s\u1ed1 c\u1ee7a \u0111\u01b0\u1eddng th\u1eb3ng d có d\u1ea1ng: <span class=\"math-tex\">$d:\\begin{cases}x=x_0+at\\\\y=y_0+bt\\\\z=z_0+ct\\end{cases}$<\/span> thì d \u0111i qua \u0111i\u1ec3m <span class=\"math-tex\">$M(x_0;y_0;z_0)$<\/span> và nh\u1eadn <span class=\"math-tex\">$\\overrightarrow{u}=(a;b;c)$<\/span> v\u1edbi <span class=\"math-tex\">$a^2+b^2+c^2\\ne0$<\/span> làm vect\u01a1 ch\u1ec9 ph\u01b0\u01a1ng.<\/p>","answer":"<p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>C.<\/strong> <span class=\"math-tex\">$\\overrightarrow{u_3}=(1;-2;3)$<\/span><\/span><\/p><p>T\u1eeb ph\u01b0\u01a1ng trình \u0111\u01b0\u1eddng th\u1eb3ng d ta th\u1ea5y vect\u01a1 <span class=\"math-tex\">$\\overrightarrow{u_3}=(1;-2;3)$<\/span> là m\u1ed9t vect\u01a1 ch\u1ec9 ph\u01b0\u01a1ng c\u1ee7a d.<\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-12-31 08:59:29","option_type":"math","len":0},{"id":"6083","post_id":"8273","mon_id":"1159285","chapter_id":"1159382","question":"<p>Trong không gian Oxyz, cho \u0111\u01b0\u1eddng th\u1eb3ng <span class=\"math-tex\">$d:\\dfrac{x-3}{2}=\\dfrac{y-4}{-5}=\\dfrac{z+1}{3}$<\/span>. Vect\u01a1 nào d\u01b0\u1edbi \u0111ây là m\u1ed9t vect\u01a1 ch\u1ec9 ph\u01b0\u01a1ng c\u1ee7a d?<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$\\overrightarrow{u_1}=(2;4;-1)$<\/span>","<strong>B.<\/strong> <span class=\"math-tex\">$\\overrightarrow{u_2}=(2;-5;3)$<\/span>","<strong>C.<\/strong> <span class=\"math-tex\">$\\overrightarrow{u_3}=(2;5;3)$<\/span>","<strong>D.<\/strong> <span class=\"math-tex\">$\\overrightarrow{u_4}=(3;4;1)$<\/span>"],"correct":"2","level":"1","hint":"<p>Trong không gian v\u1edbi h\u1ec7 tr\u1ee5c t\u1ecda \u0111\u1ed9 Oxyz, cho \u0111\u01b0\u1eddng th\u1eb3ng <span class=\"math-tex\">$d:\\dfrac{x-x_0}{a}=\\dfrac{y-y_0}{b}=\\dfrac{z-z_0}{c}$<\/span> \u0111\u01b0\u1eddng th\u1eb3ng d \u0111i qua \u0111i\u1ec3m <span class=\"math-tex\">$M(x_0; y_0;z_0)$<\/span> và có vect\u01a1 ch\u1ec9 ph\u01b0\u01a1ng <span class=\"math-tex\">$\\overrightarrow{u}=(a;b;c)$<\/span>.<\/p>","answer":"<p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>B.<\/strong> <span class=\"math-tex\">$\\overrightarrow{u_2}=(2;-5;3)$<\/span><\/span><\/p><p>\u0110\u01b0\u1eddng th\u1eb3ng <span class=\"math-tex\">$d:\\dfrac{x-3}{2}=\\dfrac{y-4}{-5}=\\dfrac{z+1}{3}$<\/span> có m\u1ed9t vect\u01a1 ch\u1ec9 ph\u01b0\u01a1ng là <span class=\"math-tex\">$\\overrightarrow{u_2}=(2;-5;3)$<\/span>.<\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-12-31 09:01:46","option_type":"math","len":0},{"id":"6085","post_id":"8273","mon_id":"1159285","chapter_id":"1159382","question":"<p>Trong không gian Oxyz, cho \u0111\u01b0\u1eddng th\u1eb3ng <span class=\"math-tex\">$d:\\dfrac{x+3}{1}=\\dfrac{y-1}{-1}=\\dfrac{z-5}{2}$<\/span>. Vect\u01a1 nào d\u01b0\u1edbi \u0111ây là m\u1ed9t vect\u01a1 ch\u1ec9 ph\u01b0\u01a1ng c\u1ee7a d?<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$\\overrightarrow{u_3}=(3;-1;5)$<\/span>","<strong>B.<\/strong> <span class=\"math-tex\">$\\overrightarrow{u_2}=(1;-1;-2)$<\/span>","<strong>C.<\/strong> <span class=\"math-tex\">$\\overrightarrow{u_4}=(-3;1;5)$<\/span>","<strong>D.<\/strong> <span class=\"math-tex\">$\\overrightarrow{u_1}=(-1;1;-2)$<\/span>"],"correct":"4","level":"1","hint":"<p>Trong không gian v\u1edbi h\u1ec7 tr\u1ee5c t\u1ecda \u0111\u1ed9 Oxyz, cho \u0111\u01b0\u1eddng th\u1eb3ng <span class=\"math-tex\">$d:\\dfrac{x-x_0}{a}=\\dfrac{y-y_0}{b}=\\dfrac{z-z_0}{c}$<\/span> \u0111\u01b0\u1eddng th\u1eb3ng d \u0111i qua \u0111i\u1ec3m <span class=\"math-tex\">$M(x_0; y_0;z_0)$<\/span> và có vect\u01a1 ch\u1ec9 ph\u01b0\u01a1ng <span class=\"math-tex\">$\\overrightarrow{u}=(a;b;c)$<\/span>.<\/p>","answer":"<p>Ch\u1ecdn Ch\u1ecdn <span style=\"color:#16a085;\"><strong>D.<\/strong> <span class=\"math-tex\">$\\overrightarrow{u_1}=(-1;1;-2)$<\/span><\/span><\/p><p>\u0110\u01b0\u1eddng th\u1eb3ng <span class=\"math-tex\">$d:\\dfrac{x+3}{1}=\\dfrac{y-1}{-1}=\\dfrac{z-5}{2}$<\/span> có m\u1ed9t vect\u01a1 ch\u1ec9 ph\u01b0\u01a1ng là <span class=\"math-tex\">$\\overrightarrow{u_1}=(-1;1;-2)$<\/span>.<\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-12-31 09:07:09","option_type":"math","len":0}]}