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HomeLớp 12Toán lớp 12 - Sách Kết nối tri thứcBài 15. Phương trình đường thẳng trong không gianBài tập trung bình
{"common":{"save":0,"post_id":"8274","level":2,"total":10,"point":10,"point_extra":0},"segment":[{"id":"6090","post_id":"8274","mon_id":"1159285","chapter_id":"1159382","question":"<p>Trong không gian Oxyz, cho \u0111\u01b0\u1eddng th\u1eb3ng d \u0111i qua \u0111i\u1ec3m <span class=\"math-tex\">$M(2;2;1)$<\/span> và có m\u1ed9t vecto ch\u1ec9 ph\u01b0\u01a1ng <span class=\"math-tex\">$\\overrightarrow{u}=(5;2;-3)$<\/span>. Ph\u01b0\u01a1ng trình c\u1ee7a d là:<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$\\begin{cases}x=2+5t\\\\y=2+2t\\\\z=-1-3t\\end{cases}$<\/span>","<strong>B.<\/strong> <span class=\"math-tex\">$\\begin{cases}x=2+5t\\\\y=2+2t\\\\z=1-3t\\end{cases}$<\/span>","<strong>C.<\/strong> <span class=\"math-tex\">$\\begin{cases}x=2+5t\\\\y=2+2t\\\\z=1+3t\\end{cases}$<\/span>","<strong>D.<\/strong> <span class=\"math-tex\">$\\begin{cases}x=5+2t\\\\y=2+2t\\\\z=-3+t\\end{cases}$<\/span>"],"correct":"2","level":"2","hint":"<p>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 thì 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>.<\/p>","answer":"<p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>B.<\/strong> <span class=\"math-tex\">$\\begin{cases}x=2+5t\\\\y=2+2t\\\\z=1-3t\\end{cases}$<\/span><\/span><\/p><p>\u0110\u01b0\u1eddng th\u1eb3ng d \u0111i qua \u0111i\u1ec3m <span class=\"math-tex\">$M(2;2;1)$<\/span> và có m\u1ed9t vecto ch\u1ec9 ph\u01b0\u01a1ng <span class=\"math-tex\">$\\overrightarrow{u}=(5;2;-3)$<\/span> thì ph\u01b0\u01a1ng trình tham s\u1ed1 c\u1ee7a d là <span class=\"math-tex\">$\\begin{cases}x=2+5t\\\\y=2+2t\\\\z=1-3t\\end{cases}$<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-12-31 09:26:58","option_type":"math","len":0},{"id":"6092","post_id":"8274","mon_id":"1159285","chapter_id":"1159382","question":"<p>Trong không gian Oxyz, cho hai \u0111i\u1ec3m M(1; 0; 1) và N(3; 2; –1). \u0110\u01b0\u1eddng th\u1eb3ng MN có ph\u01b0\u01a1ng trình tham s\u1ed1 là<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$\\begin{cases}x=1+t\\\\y=t\\\\z=1-t\\end{cases}$<\/span>","<strong>B.<\/strong> <span class=\"math-tex\">$\\begin{cases}x=1+t\\\\y=t\\\\z=1+t\\end{cases}$<\/span>","<strong>C.<\/strong> <span class=\"math-tex\">$\\begin{cases}x=1-t\\\\y=t\\\\z=1+t\\end{cases}$<\/span>","<strong>D.<\/strong> <span class=\"math-tex\">$\\begin{cases}x=1+2t\\\\y=2t\\\\z=1+t\\end{cases}$<\/span>"],"correct":"1","level":"2","hint":"<p>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 thì 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>.<\/p>","answer":"<p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>A.<\/strong> <span class=\"math-tex\">$\\begin{cases}x=1+t\\\\y=t\\\\z=1-t\\end{cases}$<\/span><\/span><\/p><p>\u0110\u01b0\u1eddng th\u1eb3ng MN nh\u1eadn <span class=\"math-tex\">$\\overrightarrow{MN}=(2;2;-2)$<\/span> ho\u1eb7c <span class=\"math-tex\">$\\overrightarrow{u}=(1;1;-1)$<\/span> là vec t\u01a1 ch\u1ec9 ph\u01b0\u01a1ng nên ta lo\u1ea1i ngay ph\u01b0\u01a1ng án B, C và D.<br \/>Thay t\u1ecda \u0111\u1ed9 \u0111i\u1ec3m M(1; 0; 1) vào ph\u01b0\u01a1ng trình \u1edf ph\u01b0\u01a1ng án A ta th\u1ea5y th\u1ecfa mãn.<\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-12-31 09:33:46","option_type":"math","len":0},{"id":"6093","post_id":"8274","mon_id":"1159285","chapter_id":"1159382","question":"<p>Trong không gian t\u1ecda \u0111\u1ed9 Oxyz, ph\u01b0\u01a1ng trình nào d\u01b0\u1edbi \u0111ây là ph\u01b0\u01a1ng trình chính t\u1eafc c\u1ee7a \u0111\u01b0\u1eddng th\u1eb3ng <span class=\"math-tex\">$d:\\begin{cases}x=1+2t\\\\y=3t\\\\z=-2+t\\end{cases}$<\/span>?<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$\\dfrac{x+1}{2}=\\dfrac{y}{3}=\\dfrac{z-2}{1}$<\/span>","<strong>B.<\/strong> <span class=\"math-tex\">$\\dfrac{x-1}{1}=\\dfrac{y}{3}=\\dfrac{z+2}{-2}$<\/span>","<strong>C.<\/strong> <span class=\"math-tex\">$\\dfrac{x-1}{2}=\\dfrac{y}{3}=\\dfrac{z+2}{1}$<\/span>","<strong>D.<\/strong> <span class=\"math-tex\">$\\dfrac{x+1}{2}=\\dfrac{y}{3}=\\dfrac{z-2}{-2}$<\/span>"],"correct":"3","level":"2","hint":"<p>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 thì ph\u01b0\u01a1ng trình chính t\u1eafc c\u1ee7a \u0111\u01b0\u1eddng th\u1eb3ng d có d\u1ea1ng <span class=\"math-tex\">$\\dfrac{x-x_0}{a}=\\dfrac{y-y_0}{b}=\\dfrac{z-z_0}{c},(a_1,a_2,a_3\\ne0)$<\/span>.<\/p>","answer":"<p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>C.<\/strong> <span class=\"math-tex\">$\\dfrac{x-1}{2}=\\dfrac{y}{3}=\\dfrac{z+2}{1}$<\/span><\/span><\/p><p>Do \u0111\u01b0\u1eddng th\u1eb3ng <span class=\"math-tex\">$d:\\begin{cases}x=1+2t\\\\y=3t\\\\z=-2+t\\end{cases}$<\/span> \u0111i qua \u0111i\u1ec3m <span class=\"math-tex\">$M(1;0;-2)$<\/span> và có véc t\u01a1 ch\u1ec9 ph\u01b0\u01a1ng <span class=\"math-tex\">$\\overrightarrow{u}=(2;3;1)$<\/span> nên có ph\u01b0\u01a1ng trình chính t\u1eafc <span class=\"math-tex\">$\\dfrac{x-1}{2}=\\dfrac{y}{3}=\\dfrac{z+2}{1}$<\/span>.<\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-12-31 09:40:34","option_type":"math","len":0}]}