Tích của vectơ với một số - Bài tập trung bình

Home Lớp 10 Toán lớp 10 - Sách Kết nối tri thức Bài 9. Tích của vectơ với một sốBài tập trung bình

{"common":{"save":0,"post_id":"6515","level":2,"total":10,"point":10,"point_extra":0},"segment":[{"id":"7220","mon_id":"1158767","chapter_id":"1158915","post_id":"6515","question":"Cho hình ch\u1eef nh\u1eadt ABCD tâm O. G\u1ecdi M, N l\u1ea7n l\u01b0\u1ee3t là trung \u0111i\u1ec3m c\u1ee7a OA và CD. Bi\u1ebft $\\overrightarrow{MN}=a.\\overrightarrow{AB}+b.\\overrightarrow{AD}$<\/span>, tính a + b. <\/p>","options":["A. $a+b=1$<\/span><\/strong>","B. $a+b=\\dfrac{1}{2}$<\/span><\/strong>","C. $a+b=\\dfrac{3}{4}$<\/span><\/strong>","D. $a+b=\\dfrac{1}{4}$<\/span><\/strong>"],"correct":"1","level":"2","hint":"","answer":"<svg height=\"175\" width=\"400\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\"> <g> <title><\/title> <rect fill=\"#fff\" height=\"177\" id=\"canvas_background\" width=\"402\" 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=\"175.00001\" id=\"svg_1\" stroke=\"null\" width=\"398.99998\" x=\"-0.5\" 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\" y=\"-1\"><\/image> <\/g> <\/svg><\/span><\/p>$\\overrightarrow{MN}=\\overrightarrow{MO}+\\overrightarrow{ON}$<\/span> $=\\dfrac{1}{4}\\overrightarrow{AC}+\\dfrac{1}{2}\\overrightarrow{AD}$<\/span> $=\\dfrac{1}{4}(\\overrightarrow{AB}+\\overrightarrow{BC})+\\dfrac{1}{2}\\overrightarrow{AD}$<\/span><\/p>$=\\dfrac{1}{4}(\\overrightarrow{AB}+\\overrightarrow{AD})+\\dfrac{1}{2}\\overrightarrow{AD}$<\/span> $=\\dfrac{1}{4}\\overrightarrow{AB}+\\dfrac{3}{4}\\overrightarrow{AD}$<\/span><\/p>Suy ra $a=\\dfrac{1}{4}$<\/span> <\/strong>và $b=\\dfrac{3}{4}$<\/span><\/strong><\/span>. V\u1eady $a+b=1$<\/span>.<\/strong><\/p>Ch\u1ecdn A. $a+b=1$<\/span><\/strong><\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2023-06-21 10:07:29","option_type":"math","len":0},{"id":"7222","mon_id":"1158767","chapter_id":"1158915","post_id":"6515","question":"Cho t\u1ee9 giác ABCD, trên c\u1ea1nh AB, CD l\u1ea5y l\u1ea7n l\u01b0\u1ee3t các \u0111i\u1ec3m M, N sao cho $3.\\overrightarrow{AM}=2.\\overrightarrow{AB}$<\/span> và $3.\\overrightarrow{DN}=2.\\overrightarrow{DC}$<\/span>. Tính vect\u01a1 $\\overrightarrow{MN}$<\/span> theo hai vect\u01a1 $\\overrightarrow{AD}$<\/span> và $\\overrightarrow{BC}$<\/span>.<\/p>","options":["A. $\\overrightarrow{MN}=\\dfrac{1}{3}\\overrightarrow{AD}+\\dfrac{1}{3}\\overrightarrow{BC}$<\/span><\/strong>","B. $\\overrightarrow{MN}=\\dfrac{1}{3}\\overrightarrow{AD}-\\dfrac{2}{3}\\overrightarrow{BC}$<\/span><\/strong>","C. $\\overrightarrow{MN}=\\dfrac{1}{3}\\overrightarrow{AD}+\\dfrac{2}{3}\\overrightarrow{BC}$<\/span><\/strong>","D. $\\overrightarrow{MN}=\\dfrac{2}{3}\\overrightarrow{AD}+\\dfrac{1}{3}\\overrightarrow{BC}$<\/span><\/strong>"],"correct":"3","level":"2","hint":"","answer":"Ta có: $\\overrightarrow{MN}=\\overrightarrow{MA}+\\overrightarrow{AD}+\\overrightarrow{DN}$<\/span> <\/p>$=\\dfrac{2}{3}\\overrightarrow{BA}+\\overrightarrow{AD}+\\dfrac{2}{3}\\overrightarrow{DC}$<\/span><\/p>$=\\dfrac{2}{3}(\\overrightarrow{BC}+\\overrightarrow{CA})+\\overrightarrow{AD}+\\dfrac{2}{3}(\\overrightarrow{DA}+\\overrightarrow{AC})$<\/span><\/p>$=\\dfrac{2}{3}\\overrightarrow{BC}+\\overrightarrow{AD}-\\dfrac{2}{3}\\overrightarrow{AD}$<\/span><\/p> $=\\dfrac{1}{3}\\overrightarrow{AD}+\\dfrac{2}{3}\\overrightarrow{BC}$<\/span><\/strong><\/p>Ch\u1ecdn C. $\\overrightarrow{MN}=\\dfrac{1}{3}\\overrightarrow{AD}+\\dfrac{2}{3}\\overrightarrow{BC}$<\/span><\/strong><\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2023-06-21 10:09:27","option_type":"math","len":0},{"id":"7224","mon_id":"1158767","chapter_id":"1158915","post_id":"6515","question":"Cho tam giác ABC. \u0110\u1eb7t $\\overrightarrow{a} = \\overrightarrow{BC}$<\/span> , $\\overrightarrow{b} = \\overrightarrow{AC}$<\/span> . Các c\u1eb7p vect\u01a1 nào sau \u0111ây cùng ph\u01b0\u01a1ng?<\/p>","options":["A.<\/strong> $2\\overrightarrow{a}+\\overrightarrow{b}$<\/span>, $\\overrightarrow{a}+2\\overrightarrow{b}$<\/span>","B.<\/strong> $\\overrightarrow{a}-2\\overrightarrow{b}$<\/span> , $2\\overrightarrow{a}-\\overrightarrow{b}$<\/span>","C.<\/strong> $5\\overrightarrow{a}+\\overrightarrow{b}$<\/span>, $-10\\overrightarrow{a}-2\\overrightarrow{b}$<\/span>","D.<\/strong> $\\overrightarrow{a}+\\overrightarrow{b}$<\/span>, $\\overrightarrow{a}-\\overrightarrow{b}$<\/span>"],"correct":"3","level":"2","hint":"","answer":"Ta có  $-10\\overrightarrow{a}-2\\overrightarrow{b}$<\/span> = –2 ($5\\overrightarrow{a}+\\overrightarrow{b}$<\/span>)<\/p>⇒  $5\\overrightarrow{a}+\\overrightarrow{b}$<\/span> và  $-10\\overrightarrow{a}-2\\overrightarrow{b}$<\/span>  là hai vect\u01a1 cùng ph\u01b0\u01a1ng.<\/p>\u0110áp án \u0111úng là   C.<\/strong> $5\\overrightarrow{a}+\\overrightarrow{b}$<\/span>, $-10\\overrightarrow{a}-2\\overrightarrow{b}$<\/span>.<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2023-06-22 01:18:42","option_type":"math","len":0}]}