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HomeLớp 12Toán lớp 12 - Sách Kết nối tri thứcBài tập cuối chương 2. VECTƠ VÀ HỆ TRỤC TOẠ ĐỘ TRONG KHÔNG GIAN.Bài tập trung bình
{"common":{"save":0,"post_id":"7595","level":2,"total":10,"point":10,"point_extra":0},"segment":[{"id":"5659","post_id":"7595","mon_id":"1159285","chapter_id":"1159392","question":"<p>Cho hai vect\u01a1 <span class=\"math-tex\">$\\overrightarrow{a}$<\/span> và <span class=\"math-tex\">$\\overrightarrow{b}$<\/span> th\u1ecfa mãn <span class=\"math-tex\">$|\\overrightarrow{a}|=3,|\\overrightarrow{b}|=2$<\/span> và <span class=\"math-tex\">$\\overrightarrow{a}.\\overrightarrow{b}=-3$<\/span>. Xác \u0111\u1ecbnh góc α gi\u1eefa hai vect\u01a1 <span class=\"math-tex\">$\\overrightarrow{a}$<\/span> và <span class=\"math-tex\">$\\overrightarrow{b}$<\/span>.<\/p>","options":["<strong>A.<\/strong> α = 30°","<strong>B.<\/strong> α = 45°","<strong>C.<\/strong> α = 60°","<strong>D.<\/strong> α = 120°"],"correct":"4","level":"2","hint":"<p><span class=\"math-tex\">$\\overrightarrow{a}.\\overrightarrow{b}=|\u200b\u200b\\overrightarrow{a}|.|\\overrightarrow{b}|.\\cos(\\overrightarrow{a},\\overrightarrow{b})$<\/span><\/p>","answer":"<p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>D.<\/strong> α = 120°<\/span><\/p><p>Ta có: <span class=\"math-tex\">$\\overrightarrow{a}.\\overrightarrow{b}=|\u200b\u200b\\overrightarrow{a}|.|\\overrightarrow{b}|.\\cos(\\overrightarrow{a},\\overrightarrow{b})$<\/span><\/p><p>⇒ <span class=\"math-tex\">$\\cos(\\overrightarrow{a},\\overrightarrow{b})=\\dfrac{\\overrightarrow{a}.\\overrightarrow{b}}{|\u200b\u200b\\overrightarrow{a}|.|\\overrightarrow{b}|}=\\dfrac{-3}{3.2}=\\dfrac{-1}{2}$<\/span> ⇒ <span class=\"math-tex\">$(\\overrightarrow{a},\\overrightarrow{b})=120^o$<\/span>.<\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-09-05 01:28:34","option_type":"txt","len":2},{"id":"5663","post_id":"7595","mon_id":"1159285","chapter_id":"1159392","question":"<p>Trong không gian cho \u0111i\u1ec3m O và b\u1ed1n \u0111i\u1ec3m A, B, C, D không th\u1eb3ng hàng. \u0110i\u1ec1u ki\u1ec7n c\u1ea7n và \u0111\u1ee7 \u0111\u1ec3 A, B, C, D t\u1ea1o thành hình bình hành là:<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$\\overrightarrow{OA}+\\overrightarrow{OB}+\\overrightarrow{OC}+\\overrightarrow{OD}=\\overrightarrow{0}$<\/span>","<strong>B.<\/strong> <span class=\"math-tex\">$\\overrightarrow{OA}+\\overrightarrow{OC}=\\overrightarrow{OB}+\\overrightarrow{OD}$<\/span>","<strong>C.<\/strong> <span class=\"math-tex\">$\\overrightarrow{OA}+\\dfrac{1}{2}\\overrightarrow{OB}=\\overrightarrow{OC}+\\dfrac{1}{2}\\overrightarrow{OD}$<\/span>","<strong>D.<\/strong> <span class=\"math-tex\">$\\overrightarrow{OA}+\\dfrac{1}{2}\\overrightarrow{OC}=\\overrightarrow{OB}+\\dfrac{1}{2}\\overrightarrow{OD}$<\/span>"],"correct":"2","level":"2","hint":"<p>S\u1eed d\u1ee5ng phép c\u1ed9ng vect\u01a1.<\/p>","answer":"<p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>B.<\/strong> <span class=\"math-tex\">$\\overrightarrow{OA}+\\overrightarrow{OC}=\\overrightarrow{OB}+\\overrightarrow{OD}$<\/span><\/span><\/p><p>Tr\u01b0\u1edbc h\u1ebft, \u0111i\u1ec1u ki\u1ec7n c\u1ea7n và \u0111\u1ee7 \u0111\u1ec3 ABCD là hình bình hành là: <span class=\"math-tex\">$\\overrightarrow{BD}=\\overrightarrow{BA}+\\overrightarrow{BC}$<\/span><\/p><p>V\u1edbi m\u1ecdi \u0111i\u1ec3m O b\u1ea5t kì khác A, B, C , D ta có:<\/p><p><span class=\"math-tex\">$\\overrightarrow{BD}=\\overrightarrow{BA}+\\overrightarrow{BC}$<\/span> ⇔ <span class=\"math-tex\">$\\overrightarrow{OD}-\\overrightarrow{OB} =\\overrightarrow{OA}-\\overrightarrow{OB}+\\overrightarrow{OC}-\\overrightarrow{OB}$<\/span><\/p><p>⇔ <span style=\"color:#16a085;\"><span class=\"math-tex\">$\\overrightarrow{OA}+\\overrightarrow{OC}=\\overrightarrow{OB}+\\overrightarrow{OD}$<\/span><\/span><\/p><p><span class=\"svgedit\"><svg height=\"170\" width=\"210\"> <g> <title><\/title> <rect fill=\"#ffffaa\" height=\"172\" id=\"canvas_background\" width=\"212\" x=\"-1\" y=\"-1\"><\/rect> <g display=\"none\" id=\"canvasGrid\"> <rect fill=\"url(#gridpattern)\" height=\"100%\" id=\"svg_9\" stroke-width=\"0\" width=\"100%\" x=\"0\" y=\"0\"><\/rect> <\/g> <\/g> <g> <title><\/title> <g id=\"svg_15\"> <g id=\"svg_8\" stroke=\"null\"> <path d=\"m19.04491,152.32028l34.32321,-53.3077l137.29281,0l-34.32321,53.3077l-137.29281,0z\" fill=\"#aaffd4\" id=\"svg_1\" stroke=\"#000\" stroke-width=\"2\"><\/path> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_2\" stroke=\"#000\" stroke-dasharray=\"5,5\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"2\" x1=\"58.828\" x2=\"52.6\" y1=\"22.21503\" y2=\"100.90734\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_3\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"2\" x1=\"58.136\" x2=\"191\" y1=\"21.36888\" y2=\"98.36887\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_5\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"2\" x1=\"18\" x2=\"58.828\" y1=\"152.52272\" y2=\"20.52272\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_6\" stroke=\"#ffffff\" stroke-dasharray=\"5,5\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-width=\"2.5\" x1=\"58.828\" x2=\"175.084\" y1=\"99.21503\" y2=\"99.21503\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_4\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"2\" x1=\"155.708\" x2=\"59.52\" y1=\"151.67657\" y2=\"23.06118\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_7\" stroke=\"#ffffff\" stroke-dasharray=\"5,5\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-width=\"2.5\" x1=\"50.524\" x2=\"22.152\" y1=\"103.4458\" y2=\"147.4458\"><\/line> <\/g> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" font-style=\"italic\" id=\"svg_10\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" x=\"40.99999\" xml:space=\"preserve\" y=\"20.52272\">O<\/text> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_11\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" x=\"56.99999\" xml:space=\"preserve\" y=\"96.52272\">A<\/text> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_12\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" x=\"191.99999\" xml:space=\"preserve\" y=\"101.52272\">D<\/text> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_13\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" x=\"163.99999\" xml:space=\"preserve\" y=\"162.52272\">C<\/text> <text fill=\"#000000\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"24\" id=\"svg_14\" stroke=\"#000\" stroke-width=\"0\" text-anchor=\"start\" x=\"-0.00001\" xml:space=\"preserve\" y=\"165.52272\">B<\/text> <\/g> <\/g> <\/svg><\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-09-05 01:52:28","option_type":"math","len":0},{"id":"5665","post_id":"7595","mon_id":"1159285","chapter_id":"1159392","question":"<p>Cho t\u1ee9 di\u1ec7n ABCD. G\u1ecdi I, J l\u1ea7n l\u01b0\u1ee3t là trung \u0111i\u1ec3m c\u1ee7a AB và CD, G là trung \u0111i\u1ec3m c\u1ee7a IJ. Cho các \u0111\u1eb3ng th\u1ee9c sau, \u0111\u1eb3ng th\u1ee9c nào <strong>\u0111úng<\/strong>?<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$\\overrightarrow{GA}+\\overrightarrow{GB}+\\overrightarrow{GC}+\\overrightarrow{GD}=\\overrightarrow{0}$<\/span>","<strong>B.<\/strong> <span class=\"math-tex\">$\\overrightarrow{GA}+\\overrightarrow{GB}+\\overrightarrow{GC}+\\overrightarrow{GD}=2\\overrightarrow{IJ}$<\/span>","<strong>C.<\/strong> <span class=\"math-tex\">$\\overrightarrow{GA}+\\overrightarrow{GB}+\\overrightarrow{GC}+\\overrightarrow{GD}=\\overrightarrow{IJ}$<\/span>","<strong>D.<\/strong> <span class=\"math-tex\">$\\overrightarrow{GA}+\\overrightarrow{GB}+\\overrightarrow{GC}+\\overrightarrow{GD}=-2\\overrightarrow{IJ}$<\/span>"],"correct":"1","level":"2","hint":"<p>S\u1eed d\u1ee5ng phép c\u1ed9ng vect\u01a1.<\/p>","answer":"<p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>A.<\/strong> <span class=\"math-tex\">$\\overrightarrow{GA}+\\overrightarrow{GB}+\\overrightarrow{GC}+\\overrightarrow{GD}=\\overrightarrow{0}$<\/span><\/span><\/p><p>Ta có: <span class=\"math-tex\">$\\overrightarrow{GA}+\\overrightarrow{GB}+\\overrightarrow{GC}+\\overrightarrow{GD}=(\\overrightarrow{GA}+\\overrightarrow{GB})+(\\overrightarrow{GC}+\\overrightarrow{GD})$<\/span><\/p><p> <span class=\"math-tex\">$=2\\overrightarrow{GI}+2\\overrightarrow{GJ}=2(\\overrightarrow{GI}+\\overrightarrow{GJ})=\\overrightarrow{0}$<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-09-05 01:53:23","option_type":"math","len":0}]}