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HomeLớp 12Toán lớp 12 - Sách Kết nối tri thứcBài 16. Công thức tính góc trong không gianBài tập cơ bản
{"common":{"save":0,"post_id":"8315","level":1,"total":10,"point":10,"point_extra":0},"segment":[{"id":"6172","post_id":"8315","mon_id":"1159285","chapter_id":"1159382","question":"<p>G\u1ecdi α là góc gi\u1eefa hai \u0111\u01b0\u1eddng th\u1eb3ng AB, CD. Kh\u1eb3ng \u0111\u1ecbnh nào sau \u0111ây là <strong>\u0111úng<\/strong>?<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$\\cos\\alpha=\\dfrac{|\\overrightarrow{AB}.\\overrightarrow{CD}|}{|\\overrightarrow{AB}|.|\\overrightarrow{CD}|}$<\/span>","<strong>B.<\/strong> <span class=\"math-tex\">$\\cos\\alpha=\\dfrac{\\overrightarrow{AB}.\\overrightarrow{CD}}{|\\overrightarrow{AB}|.|\\overrightarrow{CD}|}$<\/span>","<strong>C.<\/strong> <span class=\"math-tex\">$\\cos\\alpha=\\dfrac{\\Big|\\overrightarrow{AB}.\\overrightarrow{CD}\\Big|}{\\Big|\\Big[\\overrightarrow{AB},\\overrightarrow{CD}\\Big]\\Big|}$<\/span>","<strong>D.<\/strong> <span class=\"math-tex\">$\\cos\\alpha=\\dfrac{\\Big|\\Big[\\overrightarrow{AB},\\overrightarrow{CD}\\Big]\\Big|}{|\\overrightarrow{AB}|.|\\overrightarrow{CD}|}$<\/span>"],"correct":"1","level":"1","hint":"","answer":"<p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>A.<\/strong> <span class=\"math-tex\">$\\cos\\alpha=\\dfrac{|\\overrightarrow{AB}.\\overrightarrow{CD}|}{|\\overrightarrow{AB}|.|\\overrightarrow{CD}|}$<\/span><\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2025-01-12 09:46:20","option_type":"math","len":0},{"id":"6173","post_id":"8315","mon_id":"1159285","chapter_id":"1159382","question":"<p>Cho hai \u0111\u01b0\u1eddng th\u1eb3ng <span class=\"math-tex\">$d_1:\\begin{cases}x=2+t\\\\y=-1+t\\\\z=3\\end{cases}$<\/span> và <span class=\"math-tex\">$d_2:\\begin{cases}x=1-t\\\\y=2\\\\z=-2+t\\end{cases}$<\/span>. Góc gi\u1eefa hai \u0111\u01b0\u1eddng th\u1eb3ng <span class=\"math-tex\">$d_1$<\/span> và <span class=\"math-tex\">$d_2$<\/span> là:<\/p>","options":["<strong>A.<\/strong> 30°","<strong>B.<\/strong> 120°","<strong>C.<\/strong> 150°","<strong>D.<\/strong> 60°"],"correct":"4","level":"1","hint":"","answer":"<p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>D.<\/strong> 60°<\/span><\/p><p><span class=\"math-tex\">$d_1:\\begin{cases}x=2+t\\\\y=-1+t\\\\z=3\\end{cases}$<\/span> có VTCP là <span class=\"math-tex\">$\\overrightarrow{u_1}=(1; 1; 0)$<\/span>; <span class=\"math-tex\">$d_2:\\begin{cases}x=1-t\\\\y=2\\\\z=-2+t\\end{cases}$<\/span> có VTCP là <span class=\"math-tex\">$\\overrightarrow{u_2}=(-1;0; 1)$<\/span>.<\/p><p>Áp d\u1ee5ng công th\u1ee9c ta có:<\/p><p><span class=\"math-tex\">$\\cos(d_1,d_2)=|\\cos(\\overrightarrow{u_1},\\overrightarrow{u_2})|=\\dfrac{|\\overrightarrow{u_1}.\\overrightarrow{u_2}|}{|\\overrightarrow{u_1}|.|\\overrightarrow{u_2}|}=\\dfrac{1}{2}$<\/span><\/p><p>⇒ <span class=\"math-tex\">$(d_1,d_2)=60^o$<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2025-01-12 09:50:11","option_type":"txt","len":1},{"id":"6175","post_id":"8315","mon_id":"1159285","chapter_id":"1159382","question":"<p>Cho \u0111\u01b0\u1eddng th\u1eb3ng <span class=\"math-tex\">$d:\\dfrac{x}{1}=\\dfrac{y}{-2}=\\dfrac{z}{1}$<\/span> và m\u1eb7t ph\u1eb3ng <span class=\"math-tex\">$(P):5x+11y+2z-4=0$<\/span>. Góc gi\u1eefa \u0111\u01b0\u1eddng th\u1eb3ng d và m\u1eb7t ph\u1eb3ng (P) là:<\/p>","options":["<strong>A.<\/strong> 60°","<strong>B.<\/strong> –30°","<strong>C.<\/strong> 30°","<strong>D.<\/strong> –60°"],"correct":"3","level":"1","hint":"","answer":"<p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>C.<\/strong> 30°<\/span><\/p><p><span class=\"math-tex\">$d:\\dfrac{x}{1}=\\dfrac{y}{-2}=\\dfrac{z}{1}$<\/span> có vect\u01a1 ch\u1ec9 ph\u01b0\u01a1ng là <span class=\"math-tex\">$\\overrightarrow{u}=(1; -2;1)$<\/span>.<\/p><p><span class=\"math-tex\">$(P):5x+11y+2z-4=0$<\/span> có vect\u01a1 pháp tuy\u1ebfn là <span class=\"math-tex\">$\\overrightarrow{n}=(5;11;2)$<\/span>.<\/p><p>Áp d\u1ee5ng công th\u1ee9c ta có <\/p><p><span class=\"math-tex\">$\\sin(d,(P))=|\\cos(\\overrightarrow{u},\\overrightarrow{n})|=\\dfrac{|\\overrightarrow{u}.\\overrightarrow{n}|}{|\\overrightarrow{u}|.|\\overrightarrow{n}|}=\\dfrac{|1.5-2.11+1.2|}{\\sqrt{1^2+2^2+1^2}.\\sqrt{5^2+11^2+2^2}}=\\dfrac{1}{2}$<\/span><\/p><p>⇒ (d, (P)) = 30°.<\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2025-01-12 09:57:57","option_type":"txt","len":2}]}