Tổng và hiệu của hai vectơ - Bài tập khó số 1

Home Lớp 10 Toán lớp 10 - Sách Kết nối tri thức Bài 8: Tổng và hiệu của hai vectơBài tập nâng cao

{"common":{"save":0,"post_id":"6397","level":3,"total":10,"point":10,"point_extra":0},"segment":[{"id":"6197","mon_id":"1158767","chapter_id":"1158861","post_id":"6397","question":"Cho hình bình hành $ABCD$<\/span> . G\u1ecdi $G$<\/span> là tr\u1ecdng tâm c\u1ee7a tam giác $ABC$<\/span> . M\u1ec7nh \u0111\u1ec1 nào sau \u0111ây \u0111úng?<\/p>","options":["A. $\\overrightarrow{GA}+\\overrightarrow{GC}+\\overrightarrow{GD}=\\overrightarrow{BD}$<\/span>.","B. $\\overrightarrow{GA}+\\overrightarrow{GC}+\\overrightarrow{GD}=\\overrightarrow{CD}$<\/span>.","C. $\\overrightarrow{GA}+\\overrightarrow{GC}+\\overrightarrow{GD}=\\overrightarrow{0}$<\/span>.","D. $\\overrightarrow{GA}+\\overrightarrow{GC}+\\overrightarrow{GD}=\\overrightarrow{AD}$<\/span>. "],"correct":"3","level":"3","hint":"<svg height=\"126\" width=\"249\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\"> <g><title><\/title><rect fill=\"#fff\" height=\"128\" id=\"canvas_background\" width=\"251\" x=\"-1\" y=\"-1\"><\/rect> <g display=\"none\" height=\"100%\" id=\"canvasGrid\" overflow=\"visible\" width=\"100%\" x=\"0\" y=\"0\"> <rect fill=\"url(#gridpattern)\" height=\"100%\" stroke-width=\"0\" width=\"100%\" x=\"0\" y=\"0\"><\/rect> <\/g> <\/g> <g><title><\/title><image height=\"126\" id=\"svg_1\" width=\"249\" x=\"0\" xlink:href=\"data:image\/png;base64,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\" y=\"0\"><\/image> <\/g> <\/svg><\/span><\/p>Có $G$<\/span> là tr\u1ecdng tâm c\u1ee7a tam giác  $ABC$<\/span><\/p>$\\Rightarrow\\overrightarrow{GA}+\\overrightarrow{GC}+\\overrightarrow{GD}=\\overrightarrow{0}\\Rightarrow\\overrightarrow{GA}+\\overrightarrow{GC}=-\\overrightarrow{GB}\\Rightarrow\\overrightarrow{GA}+\\overrightarrow{GC}+\\overrightarrow{GD}=\\overrightarrow{GD}-\\overrightarrow{GB}=\\overrightarrow{BD}$<\/span><\/p>","answer":"\u0110áp án: A<\/strong><\/span><\/p>","type":"choose","extra_type":"classic","user_id":"147","test":"0","date":"2022-12-29 07:29:13","option_type":"math","len":0},{"id":"6198","mon_id":"1158767","chapter_id":"1158861","post_id":"6397","question":"Cho hình ch\u1eef $ABCD$<\/span> . Kh\u1eb3ng \u0111\u1ecbnh nào sau \u0111ây \u0111úng?<\/p>","options":["A. $\\overrightarrow{AC}=\\overrightarrow{BD}$<\/span>.","B. $\\overrightarrow{AB}+\\overrightarrow{AC}+\\overrightarrow{AD}=\\overrightarrow{0}$<\/span>.","C. $|\\overrightarrow{AB}-\\overrightarrow{AD}|=|\\overrightarrow{AB}+\\overrightarrow{AD}|$<\/span>.","D. $|\\overrightarrow{BC}+\\overrightarrow{BD}|=|\\overrightarrow{AC}-\\overrightarrow{AB}|$<\/span>. "],"correct":"3","level":"3","hint":"<svg height=\"166\" width=\"249\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\"> <g><title><\/title><rect fill=\"#fff\" height=\"168\" id=\"canvas_background\" width=\"251\" x=\"-1\" y=\"-1\"><\/rect> <g display=\"none\" height=\"100%\" id=\"canvasGrid\" overflow=\"visible\" width=\"100%\" x=\"0\" y=\"0\"> <rect fill=\"url(#gridpattern)\" height=\"100%\" stroke-width=\"0\" width=\"100%\" x=\"0\" y=\"0\"><\/rect> <\/g> <\/g> <g><title><\/title><image height=\"166\" id=\"svg_1\" width=\"249\" x=\"0\" xlink:href=\"data:image\/png;base64,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\" y=\"0\"><\/image> <\/g> <\/svg><\/span><\/p> $|\\overrightarrow{AB}-\\overrightarrow{AD}|=|\\overrightarrow{AB}+\\overrightarrow{AD}|\\Leftrightarrow|\\overrightarrow{DB}|=|\\overrightarrow{AC}|\\Leftrightarrow\\overrightarrow{BD}=\\overrightarrow{AC}$<\/span> (luôn \u0111úng)<\/p>","answer":"\u0110áp án: C<\/strong><\/span><\/p>","type":"choose","extra_type":"classic","user_id":"147","test":"0","date":"2022-12-29 07:41:19","option_type":"math","len":0},{"id":"6199","mon_id":"1158767","chapter_id":"1158861","post_id":"6397","question":"Cho tam giác $ABC$<\/span>  có $M$<\/span>  th\u1ecfa mãn \u0111i\u1ec1u ki\u1ec7n  $\\overrightarrow{MA}+\\overrightarrow{MB}+\\overrightarrow{MC}=\\overrightarrow{0}$<\/span>  . Xác \u0111\u1ecbnh v\u1ecb trí \u0111i\u1ec3m $M$<\/span>  .<\/p>","options":["A. $M$<\/span> là \u0111i\u1ec3m th\u1ee9 t\u01b0 c\u1ee7a hình bình hành $ABCM$<\/span> .","B. $M$<\/span> là trung \u0111i\u1ec3m c\u1ee7a \u0111o\u1ea1n th\u1eb3ng $AB$<\/span> .","C. $M$<\/span> trùng v\u1edbi $C$<\/span>.","D. $M$<\/span> là tr\u1ecdng tâm tam giác $ABC$<\/span> ."],"correct":"4","level":"3","hint":"","answer":"\u0110áp án: D<\/strong><\/span> (theo tính ch\u1ea5t véc t\u01a1 c\u1ee7a tr\u1ecdng tâm tam giác)<\/p>","type":"choose","extra_type":"classic","user_id":"147","test":"0","date":"2022-12-29 07:44:15","option_type":"math","len":0}]}