Chú ý: Để đảm bảo quyền lợi và bảo vệ tài khoản của mình
Bạn hãy xác thực địa chỉ email đăng ký nhé. Chi tiết xem tại đây
Bạn hãy xác thực địa chỉ email đăng ký nhé. Chi tiết xem tại đây
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}]}