{"common":{"save":0,"post_id":"7298","level":1,"total":10,"point":10,"point_extra":0},"segment":[{"id":"7474","mon_id":"1158767","chapter_id":"1159256","post_id":"7298","question":"<p>Cho 3 \u0111i\u1ec3m ph&acirc;n bi\u1ec7t A, B, C tho\u1ea3 m&atilde;n&nbsp;<span class=\"math-tex\">$3\\overrightarrow{AC}+2\\overrightarrow{AB}=\\overrightarrow{0}$<\/span>. 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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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}]}