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T&igrave;m kh\u1eb3ng \u0111\u1ecbnh \u0111&uacute;ng.<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$|\\overrightarrow{AB}|=\\dfrac{3}{5}|\\overrightarrow{BC}|$<\/span>","<strong>B.<\/strong> <span class=\"math-tex\">$|\\overrightarrow{AB}|=\\dfrac{3}{2}|\\overrightarrow{BC}|$<\/span>","<strong>C.<\/strong> <span class=\"math-tex\">$|\\overrightarrow{AB}|=\\dfrac{2}{5}|\\overrightarrow{BC}|$<\/span>","<strong>D.<\/strong> <span class=\"math-tex\">$|\\overrightarrow{AB}|=\\dfrac{2}{3}|\\overrightarrow{BC}|$<\/span>"],"correct":"1","level":"0","hint":"","answer":"<p><span class=\"math-tex\">$3\\overrightarrow{AC}+2\\overrightarrow{AB}=\\overrightarrow{0}$<\/span>&nbsp;<\/p><p>&hArr;&nbsp;<span class=\"math-tex\">$3(\\overrightarrow{AB}+\\overrightarrow{BC})+2\\overrightarrow{AB}=\\overrightarrow{0}$<\/span><\/p><p>&hArr;&nbsp;<span class=\"math-tex\">$5\\overrightarrow{AB}=-3\\overrightarrow{BC}$<\/span><\/p><p>&hArr;&nbsp;<span class=\"math-tex\">$\\overrightarrow{AB}=\\dfrac{-3}{5}\\overrightarrow{BC}$<\/span><\/p><p>&rArr;&nbsp;<span class=\"math-tex\">$|\\overrightarrow{AB}|=\\dfrac{3}{5}|\\overrightarrow{BC}|$<\/span><\/p><p>Ch\u1ecdn&nbsp;<span style=\"color:#16a085;\"><strong>A.<\/strong>&nbsp;<span class=\"math-tex\">$|\\overrightarrow{AB}|=\\dfrac{3}{5}|\\overrightarrow{BC}|$<\/span>.<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-04-14 01:22:21","option_type":"math","len":0},{"id":"7476","mon_id":"1158767","chapter_id":"1159256","post_id":"7298","question":"<p>G\u1ecdi C l&agrave; trung \u0111i\u1ec3m c\u1ee7a AB. T&igrave;m kh\u1eb3ng \u0111\u1ecbnh \u0111&uacute;ng.<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$\\overrightarrow{CB}=\\overrightarrow{CA}$<\/span>","<strong>B.<\/strong> <span class=\"math-tex\">$|\\overrightarrow{AB}|=|\\overrightarrow{CB}|$<\/span>","<strong>C.<\/strong> <span class=\"math-tex\">$\\overrightarrow{AB}$<\/span> v&agrave; <span class=\"math-tex\">$\\overrightarrow{AC}$<\/span> c&ugrave;ng h\u01b0\u1edbng.","<strong>D.<\/strong> <span class=\"math-tex\">$\\overrightarrow{AB}$<\/span> v&agrave; <span class=\"math-tex\">$\\overrightarrow{CB}$<\/span> ng\u01b0\u1ee3c h\u01b0\u1edbng."],"correct":"3","level":"0","hint":"","answer":"<p><span class=\"svgedit\"><svg height=\"100\" width=\"300\"> <g>&lt;title&gt;&lt;\/title><rect fill=\"#fff\" height=\"102\" id=\"canvas_background\" width=\"302\" 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>&lt;title&gt;&lt;\/title><line fill=\"none\" id=\"svg_1\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"1.5\" x1=\"11.5\" x2=\"142.5\" y1=\"48.25\" y2=\"48.25\"><\/line> <line fill=\"none\" id=\"svg_2\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"1.5\" x1=\"148.5\" x2=\"279.5\" y1=\"48.25\" y2=\"48.25\"><\/line> <ellipse cx=\"147\" cy=\"48.75\" fill=\"#ff0000\" id=\"svg_3\" rx=\"3.5\" ry=\"3.5\" stroke=\"#000\" stroke-width=\"1.5\"><\/ellipse> <ellipse cx=\"280\" cy=\"48.75\" fill=\"#ff0000\" id=\"svg_4\" rx=\"3.5\" ry=\"3.5\" stroke=\"#000\" stroke-width=\"1.5\"><\/ellipse> <ellipse cx=\"12\" cy=\"48.75\" fill=\"#ff0000\" id=\"svg_5\" rx=\"3.5\" ry=\"3.5\" stroke=\"#000\" stroke-width=\"1.5\"><\/ellipse> <line fill=\"none\" id=\"svg_6\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"84.5\" x2=\"80.5\" y1=\"41.25\" y2=\"55.25\"><\/line> <line fill=\"none\" id=\"svg_8\" stroke=\"#000\" stroke-linecap=\"null\" stroke-linejoin=\"null\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"219.5\" x2=\"215.5\" y1=\"41.25\" y2=\"55.25\"><\/line> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"18\" id=\"svg_9\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"4.5\" xml:space=\"preserve\" y=\"39.25\">A<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"18\" id=\"svg_10\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"139.5\" xml:space=\"preserve\" y=\"38.25\">C<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"18\" id=\"svg_11\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"274.5\" xml:space=\"preserve\" y=\"37.25\">B<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"25\" id=\"svg_12\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"133.5\" xml:space=\"preserve\" y=\"57.25\">&gt;<\/text> <text fill=\"#000000\" fill-opacity=\"null\" font-family=\"Helvetica, Arial, sans-serif\" font-size=\"25\" id=\"svg_13\" stroke=\"#000\" stroke-opacity=\"null\" stroke-width=\"0\" text-anchor=\"start\" x=\"268.5\" xml:space=\"preserve\" y=\"57.25\">&gt;<\/text> <\/g> <\/svg><\/span><\/p><p>Suy ra ch\u1ecdn&nbsp;<span style=\"color:#16a085;\"><strong>C.<\/strong>&nbsp;<span class=\"math-tex\">$\\overrightarrow{AB}$<\/span>&nbsp;v&agrave;&nbsp;<span class=\"math-tex\">$\\overrightarrow{AC}$<\/span>&nbsp;c&ugrave;ng h\u01b0\u1edbng.<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-04-14 01:29:56","option_type":"math","len":0},{"id":"7481","mon_id":"1158767","chapter_id":"1159256","post_id":"7298","question":"<p>Cho tam gi&aacute;c ABC vu&ocirc;ng t\u1ea1i A, c&oacute; tr\u1ecdng t&acirc;m G v&agrave; BC = 12. Khi \u0111&oacute; vect\u01a1&nbsp;t\u1ed5ng&nbsp;<span class=\"math-tex\">$\\overrightarrow{GB}+\\overrightarrow{GC}$<\/span>&nbsp;c&oacute; \u0111\u1ed9 d&agrave;i b\u1eb1ng bao nhi&ecirc;u?<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$2\\sqrt{3}$<\/span>","<strong>B.<\/strong> <span class=\"math-tex\">$2$<\/span>","<strong>C.<\/strong> <span class=\"math-tex\">$4$<\/span>","<strong>D.<\/strong> <span class=\"math-tex\">$8$<\/span>"],"correct":"3","level":"0","hint":"<p>Trong tam gi&aacute;c vu&ocirc;ng, \u0111\u01b0\u1eddng trung tuy\u1ebfn \u1ee9ng v\u1edbi c\u1ea1nh huy\u1ec1n b\u1eb1ng n\u1eeda c\u1ea1nh huy\u1ec1n.<\/p>","answer":"<p><span class=\"svgedit\"><svg height=\"170\" width=\"270\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\"> <g>&lt;title&gt;&lt;\/title><rect fill=\"#fff\" height=\"172\" id=\"canvas_background\" width=\"272\" 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>&lt;title&gt;&lt;\/title><image height=\"162\" id=\"svg_1\" width=\"265\" x=\"1.5\" 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y=\"1\"><\/image> <line fill=\"none\" id=\"svg_2\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"1.5\" x1=\"87.5\" x2=\"244.5\" y1=\"27.5\" y2=\"140.5\"><\/line> <line fill=\"none\" id=\"svg_3\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"1.5\" x1=\"87.5\" x2=\"25.5\" y1=\"27.5\" y2=\"119.5\"><\/line> <line fill=\"none\" id=\"svg_4\" stroke=\"#000\" stroke-dasharray=\"5,5\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"1.5\" x1=\"86.5\" x2=\"121.5\" y1=\"28.5\" y2=\"96.5\"><\/line> <line fill=\"none\" id=\"svg_7\" stroke=\"#000\" stroke-dasharray=\"5,5\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-width=\"1.5\" x1=\"121\" x2=\"56\" y1=\"97.25\" y2=\"73.25\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_8\" stroke=\"#000\" stroke-dasharray=\"5,5\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"167\" x2=\"121\" y1=\"87.25\" y2=\"96.25\"><\/line> <line fill=\"none\" fill-opacity=\"null\" id=\"svg_9\" stroke=\"#000\" stroke-linecap=\"undefined\" stroke-linejoin=\"undefined\" stroke-opacity=\"null\" stroke-width=\"1.5\" x1=\"25\" x2=\"244\" y1=\"120.25\" y2=\"140.25\"><\/line> <rect fill=\"none\" height=\"12\" id=\"svg_10\" stroke=\"#ff0000\" stroke-width=\"1.5\" transform=\"rotate(35 89.00000000000001,35.25000000000001) \" width=\"12\" x=\"83\" y=\"29.25\"><\/rect> <\/g> <\/svg><\/span><\/p><p>G\u1ecdi I l&agrave; trung \u0111i\u1ec3m c\u1ee7a BC.<\/p><p>Ta c&oacute;&nbsp;<span class=\"math-tex\">$\\overrightarrow{GB}+\\overrightarrow{GC}$<\/span>&nbsp;<span class=\"math-tex\">$=2\\overrightarrow{GI}$<\/span>&nbsp;<span class=\"math-tex\">$=2.\\dfrac{1}{3}\\overrightarrow{AI}$<\/span>&nbsp;<span class=\"math-tex\">$=\\dfrac{2}{3}\\overrightarrow{AI}$<\/span>.<\/p><p>Suy ra&nbsp;<span class=\"math-tex\">$|\\overrightarrow{GB}+\\overrightarrow{GC}|=\\dfrac{2}{3}|\\overrightarrow{AI}|$<\/span>&nbsp;<span class=\"math-tex\">$=\\dfrac{2}{3}AI=\\dfrac{2}{3}.\\dfrac{1}{2}BC=\\dfrac{1}{3}.12=4$<\/span>&nbsp;.<\/p><p>Ch\u1ecdn&nbsp;<span style=\"color:#16a085;\"><strong>C.<\/strong>&nbsp;<span class=\"math-tex\">$4$<\/span>.<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-04-14 01:43:21","option_type":"math","len":0}]}
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