{"common":{"save":0,"post_id":"6457","level":1,"total":10,"point":10,"point_extra":0},"segment":[{"id":"6979","mon_id":"1158767","chapter_id":"1158890","post_id":"6457","question":"<p>Cho tam gi&aacute;c ABC&nbsp;c&oacute; BC = 3, CA = 5, AB = 6.&nbsp;G\u1ecdi M&nbsp;l&agrave; trung \u0111i\u1ec3m c\u1ea1nh BC.&nbsp;T&iacute;nh&nbsp;<span class=\"math-tex\">$\\overrightarrow{AM}.\\overrightarrow{BC}$<\/span>.<\/p>","options":["<strong>A. <\/strong><span class=\"math-tex\">$-\\dfrac{11}{2}$<\/span>","<strong>B.<\/strong> <span class=\"math-tex\">$\\dfrac{61}{2}$<\/span>","<strong>C. <\/strong><span class=\"math-tex\">$\\dfrac{70}{3}$<\/span>","<strong>D.<\/strong> 26"],"correct":"1","level":"1","hint":"","answer":"<p>V&igrave; M l&agrave; trung \u0111i\u1ec3m c\u1ee7a BC n&ecirc;n&nbsp;<span class=\"math-tex\">$2\\overrightarrow{AM}=\\overrightarrow{AB}+\\overrightarrow{AC}$<\/span><\/p><p>&rArr;&nbsp;<span class=\"math-tex\">$\\overrightarrow{AM}=\\dfrac{1}{2} \\bigg(\\overrightarrow{AB} + \\overrightarrow{AC} \\bigg)$<\/span><\/p><p>&Aacute;p d\u1ee5ng quy t\u1eafc tr\u1eeb ba \u0111i\u1ec3m ta c&oacute;:&nbsp;<span class=\"math-tex\">$\\overrightarrow{BC}=\\overrightarrow{AC}-\\overrightarrow{AB}$<\/span>.<\/p><p>Suy ra <span class=\"math-tex\">$\\overrightarrow{AM}.\\overrightarrow{BC}$<\/span>&nbsp;=&nbsp;<span class=\"math-tex\">$\\dfrac{1}{2}$<\/span>&nbsp;<span class=\"math-tex\">$\\bigg( \\overrightarrow{AB}+\\overrightarrow{AC}\\bigg) . \\bigg( \\overrightarrow{AC}-\\overrightarrow{AB}\\bigg) $<\/span>&nbsp;<\/p><p>=&nbsp;<span class=\"math-tex\">$\\dfrac{1}{2} \\bigg[ \\bigg( \\overrightarrow{AC}\\bigg)^2 - \\bigg( \\overrightarrow{AB}\\bigg)^2 \\bigg] = \\dfrac{1}{2}(AC^2 - AB^2)$<\/span>&nbsp;<\/p><p>=&nbsp;<span class=\"math-tex\">$\\dfrac{1}{2}(5^2 - 6^2)$<\/span>&nbsp;=&nbsp;<span class=\"math-tex\">$-\\dfrac{11}{2}$<\/span><\/p><p>\u0110&aacute;p &aacute;n \u0111&uacute;ng l&agrave;&nbsp; &nbsp;&nbsp;<span style=\"color:#16a085;\"><strong>A.&nbsp;<\/strong><span class=\"math-tex\">$-\\dfrac{11}{2}$<\/span>.<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2023-05-31 04:56:34","option_type":"math","len":0},{"id":"6981","mon_id":"1158767","chapter_id":"1158890","post_id":"6457","question":"<p>Cho h&igrave;nh vu&ocirc;ng ABCD c\u1ea1nh 4. T&iacute;nh&nbsp;<span class=\"math-tex\">$\\overrightarrow{AB}.\\overrightarrow{AC}$<\/span>&nbsp;.<\/p>","options":["<strong>A.<\/strong> 16","<strong>B.<\/strong> 0","<strong>C.<\/strong> 8<span class=\"math-tex\">$\\sqrt{2}$<\/span>","<strong>D.<\/strong> 8"],"correct":"1","level":"1","hint":"","answer":"<p><span class=\"svgedit\"><svg height=\"160\" width=\"160\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\"> <g>&lt;title&gt;&lt;\/title><rect fill=\"#fff\" height=\"162\" id=\"canvas_background\" width=\"162\" x=\"-1\" y=\"-1\"><\/rect> <g display=\"none\" height=\"100%\" id=\"canvasGrid\" overflow=\"visible\" width=\"100%\" x=\"0\" y=\"0\"> <rect fill=\"url(#gridpattern)\" height=\"100%\" stroke-width=\"0\" width=\"100%\" x=\"0\" y=\"0\"><\/rect> <\/g> <\/g> <g>&lt;title&gt;&lt;\/title><image height=\"146\" id=\"svg_1\" width=\"153\" x=\"1.5\" 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y=\"6\"><\/image> <\/g> <\/svg><\/span><\/p><p>* Theo \u0111\u1ecbnh ngh\u0129a t&iacute;ch v&ocirc; h\u01b0\u1edbng c\u1ee7a hai vect\u01a1 ta c&oacute;:<\/p><p><span class=\"math-tex\">$\\overrightarrow{AB}.\\overrightarrow{AC}=|\\overrightarrow{AB}|.|\\overrightarrow{AC}|.cos\\bigg(\\overrightarrow{AB},\\overrightarrow{AC}\\bigg)$<\/span>&nbsp;= AB . AC . cos<span class=\"math-tex\">$\\bigg(\\overrightarrow{AB},\\overrightarrow{AC}\\bigg)$<\/span><\/p><p>= 4 . 4<span class=\"math-tex\">$\\sqrt{2}$<\/span>&nbsp;. cos<span class=\"math-tex\">$\\bigg(\\overrightarrow{AB},\\overrightarrow{AC}\\bigg)$<\/span>&nbsp;= 16<span class=\"math-tex\">$\\sqrt{2}$<\/span>&nbsp;. cos<span class=\"math-tex\">$\\bigg(\\overrightarrow{AB},\\overrightarrow{AC}\\bigg)$<\/span><\/p><p>M&agrave;&nbsp;<span class=\"math-tex\">$\\bigg(\\overrightarrow{AB},\\overrightarrow{AC}\\bigg)$<\/span>&nbsp;=&nbsp;<span class=\"math-tex\">$\\widehat{BAC}$<\/span>&nbsp;= 45&deg;. Suy ra&nbsp;<span class=\"math-tex\">$\\overrightarrow{AB}.\\overrightarrow{AC}$<\/span>&nbsp;= 16<span class=\"math-tex\">$\\sqrt{2}$<\/span>&nbsp;. cos 45&deg; = 16<span class=\"math-tex\">$\\sqrt{2}$<\/span>&nbsp;.&nbsp;<span class=\"math-tex\">$\\dfrac{\\sqrt{2}}{2}$<\/span>&nbsp;=&nbsp;16&nbsp;.&nbsp;<\/p><p>\u0110&aacute;p &aacute;n \u0111&uacute;ng l&agrave;&nbsp; &nbsp;<span style=\"color:#16a085;\"><strong>A.<\/strong> 16.<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2023-05-31 05:03:07","option_type":"math","len":0},{"id":"6989","mon_id":"1158767","chapter_id":"1158890","post_id":"6457","question":"<p>Cho h&igrave;nh vu&ocirc;ng ABCD c\u1ea1nh b\u1eb1ng 4. \u0110i\u1ec3m M n\u1eb1m tr&ecirc;n \u0111o\u1ea1n th\u1eb3ng AC sao cho&nbsp;<span class=\"math-tex\">$AM = \\dfrac{AC}{4}$<\/span>&nbsp;. G\u1ecdi N l&agrave; trung \u0111i\u1ec3m c\u1ee7a \u0111o\u1ea1n th\u1eb3ng DC. T&iacute;nh&nbsp;<span class=\"math-tex\">$\\overrightarrow{MB}.\\overrightarrow{MN}$<\/span>.<\/p>","options":["<strong>A.<\/strong> &ndash;8","<strong>B.<\/strong> 0","<strong>C.<\/strong> 8","<strong>D. <\/strong>16"],"correct":"2","level":"1","hint":"","answer":"<p><span class=\"svgedit\"><svg height=\"200\" width=\"200\" xmlns:xlink=\"http:\/\/www.w3.org\/1999\/xlink\"> <g>&lt;title&gt;&lt;\/title><rect fill=\"#fff\" height=\"202\" id=\"canvas_background\" width=\"202\" x=\"-1\" y=\"-1\"><\/rect> <g display=\"none\" height=\"100%\" id=\"canvasGrid\" overflow=\"visible\" width=\"100%\" x=\"0\" y=\"0\"> <rect fill=\"url(#gridpattern)\" height=\"100%\" stroke-width=\"0\" width=\"100%\" x=\"0\" y=\"0\"><\/rect> <\/g> <\/g> <g>&lt;title&gt;&lt;\/title><image height=\"195\" id=\"svg_1\" width=\"198\" x=\"0.99999\" 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\" y=\"0.5\"><\/image> <\/g> <\/svg><\/span><\/p><p>Ta ph&acirc;n t&iacute;ch c&aacute;c vect\u01a1&nbsp;<span class=\"math-tex\">$\\overrightarrow{MB}, \\overrightarrow{MN}$<\/span>&nbsp; theo c&aacute;c vect\u01a1 c&oacute; \u0111i\u1ec3m \u0111\u1ea7u v&agrave; \u0111i\u1ec3m cu\u1ed1i l&agrave; c&aacute;c \u0111\u1ec9nh c\u1ee7a h&igrave;nh vu&ocirc;ng.<\/p><p>T\u1eeb \u0111&oacute; d\u1ef1a v&agrave;o c&aacute;c y\u1ebfu t\u1ed1 c\u1ee7a h&igrave;nh vu&ocirc;ng \u0111\u1ec3 t&iacute;nh&nbsp;<span class=\"math-tex\">$\\overrightarrow{MB}.\\overrightarrow{MN}$<\/span>.<\/p><p><span class=\"math-tex\">$\\overrightarrow{MB}=\\overrightarrow{AB}-\\overrightarrow{AM}$<\/span>&nbsp;(theo quy t\u1eafc tr\u1eeb ba \u0111i\u1ec3m)<\/p><p>=&nbsp;<span class=\"math-tex\">$\\overrightarrow{AB}-\\dfrac{1}{4}\\overrightarrow{AC}$<\/span>&nbsp;(M n\u1eb1m tr&ecirc;n \u0111o\u1ea1n th\u1eb3ng AC sao cho&nbsp;<span class=\"math-tex\">$AM = \\dfrac{AC}{4}$<\/span>)<\/p><p>=&nbsp;<span class=\"math-tex\">$\\overrightarrow{AB}-\\dfrac{1}{4}\\bigg(\\overrightarrow{AB}+\\overrightarrow{AD}\\bigg)$<\/span>&nbsp;(theo quy t\u1eafc h&igrave;nh b&igrave;nh h&agrave;nh)<\/p><p>=&nbsp;<span class=\"math-tex\">$\\dfrac{3}{4}\\overrightarrow{AB}-\\dfrac{1}{4}\\overrightarrow{AD}$<\/span>&nbsp;.<\/p><p><span class=\"math-tex\">$\\overrightarrow{MN}=\\overrightarrow{AN}-\\overrightarrow{AM}$<\/span>&nbsp;(theo quy t\u1eafc tr\u1eeb ba \u0111i\u1ec3m)<\/p><p>=&nbsp;<span class=\"math-tex\">$\\overrightarrow{AN}-\\dfrac{1}{4}\\overrightarrow{AC}$<\/span>&nbsp;(M n\u1eb1m tr&ecirc;n \u0111o\u1ea1n th\u1eb3ng AC sao cho&nbsp;<span class=\"math-tex\">$AM = \\dfrac{AC}{4}$<\/span>)<\/p><p>=&nbsp;<span class=\"math-tex\">$\\overrightarrow{AD}+\\overrightarrow{DN}-\\dfrac{1}{4}\\bigg(\\overrightarrow{AB}+\\overrightarrow{AD}\\bigg)$<\/span>&nbsp;(theo quy t\u1eafc h&igrave;nh b&igrave;nh h&agrave;nh, quy t\u1eafc c\u1ed9ng ba \u0111i\u1ec3m)<\/p><p>=&nbsp;<span class=\"math-tex\">$\\overrightarrow{AD}+\\dfrac{1}{2}\\overrightarrow{AB}-\\dfrac{1}{4}\\bigg(\\overrightarrow{AB}+\\overrightarrow{AD}\\bigg)$<\/span>&nbsp;(v&igrave; N l&agrave; trung \u0111i\u1ec3m c\u1ee7a \u0111o\u1ea1n th\u1eb3ng DC n&ecirc;n&nbsp;<span class=\"math-tex\">$\\overrightarrow{DN}=\\dfrac{1}{2}\\overrightarrow{AB}$<\/span>&nbsp;)<\/p><p>=&nbsp;<span class=\"math-tex\">$\\dfrac{3}{4}\\overrightarrow{AD}+\\dfrac{1}{4}\\overrightarrow{AB}$<\/span>&nbsp;.<\/p><p>Ta c&oacute;&nbsp;<span class=\"math-tex\">$\\overrightarrow{MB}.\\overrightarrow{MN}$<\/span>&nbsp;= <span class=\"math-tex\">$\\bigg(\\dfrac{3}{4}\\overrightarrow{AB}-\\dfrac{1}{4}\\overrightarrow{AD}\\bigg)$<\/span>&nbsp;.&nbsp;<span class=\"math-tex\">$\\bigg(\\dfrac{3}{4}\\overrightarrow{AD}+\\dfrac{1}{4}\\overrightarrow{AB}\\bigg)$<\/span><\/p><p>=&nbsp;<span class=\"math-tex\">$\\dfrac{9}{16}\\overrightarrow{AB}.\\overrightarrow{AD}+\\dfrac{3}{16}\\bigg(\\overrightarrow{AB}\\bigg)^2-\\dfrac{3}{16}\\bigg(\\overrightarrow{AD}\\bigg)^2-\\dfrac{1}{16}\\overrightarrow{AD}.\\overrightarrow{AB}$<\/span><\/p><p>V&igrave; AB&nbsp;<span class=\"math-tex\">$\\bot$<\/span>&nbsp;AD n&ecirc;n&nbsp;<span class=\"math-tex\">$\\overrightarrow{AB}.\\overrightarrow{AD}$<\/span>&nbsp;= 0;&nbsp;<span class=\"math-tex\">$\\bigg(\\overrightarrow{AB}\\bigg)^2$<\/span>&nbsp;= AB&sup2; = 16;&nbsp;<span class=\"math-tex\">$\\bigg(\\overrightarrow{AD}\\bigg)^2$<\/span>&nbsp;= AD&sup2; = 16.<\/p><p>Do \u0111&oacute;&nbsp;<span class=\"math-tex\">$\\overrightarrow{MB}.\\overrightarrow{MN}$<\/span>&nbsp;= 0.<\/p><p>\u0110&aacute;p &aacute;n \u0111&uacute;ng l&agrave;&nbsp; &nbsp;&nbsp;<span style=\"color:#16a085;\"><strong>B.<\/strong> 0.<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2023-05-31 08:42:34","option_type":"txt","len":1}]}