{"common":{"save":0,"post_id":"6459","level":2,"total":10,"point":10,"point_extra":0},"segment":[{"id":"7025","mon_id":"1158767","chapter_id":"1158890","post_id":"6459","question":"<p>Trong m\u1eb7t ph\u1eb3ng t\u1ecda \u0111\u1ed9 Oxy, cho b\u1ed1n \u0111i\u1ec3m A(&ndash;2;&nbsp;&ndash;5), B(6;&nbsp;&ndash;1), C(3;&nbsp;&ndash;10) v&agrave; D(8;&nbsp;&ndash;5).<\/p><p>Kh\u1eb3ng \u0111\u1ecbnh n&agrave;o sau \u0111&acirc;y l&agrave; <strong>\u0111&uacute;ng<\/strong>?<\/p>","options":["<strong>A.<\/strong> G&oacute;c BAD v&agrave; g&oacute;c BCD ph\u1ee5 nhau.","<strong>B.<\/strong> G&oacute;c BCD l&agrave; g&oacute;c t&ugrave;.","<strong>C.<\/strong> cos<span class=\"math-tex\">$\\bigg(\\overrightarrow{AB},\\overrightarrow{AD}\\bigg)$<\/span> = cos<span class=\"math-tex\">$\\bigg(\\overrightarrow{CB},\\overrightarrow{CD}\\bigg)$<\/span>.","<strong>D.<\/strong> G&oacute;c BAD v&agrave; g&oacute;c BCD b&ugrave; nhau."],"correct":"3","level":"2","hint":"","answer":"<p>Ta c&oacute;&nbsp;&nbsp;<span class=\"math-tex\">$\\overrightarrow{AB}$<\/span>&nbsp;= (8; 4) ;&nbsp;<span class=\"math-tex\">$\\overrightarrow{AD}$<\/span>&nbsp;= (10; 0) ;&nbsp;<span class=\"math-tex\">$\\overrightarrow{CB}$<\/span>&nbsp;= (3; 9) ;&nbsp;<span class=\"math-tex\">$\\overrightarrow{CD}$<\/span>&nbsp;= (5; 5) .<\/p><p>cos<span class=\"math-tex\">$\\bigg(\\overrightarrow{AB},\\overrightarrow{AD}\\bigg)$<\/span>&nbsp;=&nbsp;<span class=\"math-tex\">$\\dfrac{\\overrightarrow{AB},\\overrightarrow{AD}}{|\\overrightarrow{AB}|.|\\overrightarrow{AD}|}$<\/span>&nbsp;=&nbsp;<span class=\"math-tex\">$\\dfrac{8.10+4.0}{\\sqrt{8^2+4^2}.\\sqrt{10^2+0^2}}$<\/span>&nbsp;=&nbsp;<span class=\"math-tex\">$\\dfrac{2\\sqrt{5}}{5}$<\/span>&nbsp;.<\/p><p>cos<span class=\"math-tex\">$\\bigg(\\overrightarrow{CB},\\overrightarrow{CD}\\bigg)$<\/span>=&nbsp;<span class=\"math-tex\">$\\dfrac{\\overrightarrow{CB},\\overrightarrow{CD}}{|\\overrightarrow{CB}|.|\\overrightarrow{CD}|}$<\/span>&nbsp;=&nbsp;<span class=\"math-tex\">$\\dfrac{3.5+9.5}{\\sqrt{3^2+9^2}.\\sqrt{5^2+5^2}}$<\/span>&nbsp;=&nbsp;<span class=\"math-tex\">$\\dfrac{2\\sqrt{5}}{5}$<\/span>&nbsp;.<\/p><p>Suy ra&nbsp;&nbsp;&nbsp;cos<span class=\"math-tex\">$\\bigg(\\overrightarrow{AB},\\overrightarrow{AD}\\bigg)$<\/span>&nbsp; = cos<span class=\"math-tex\">$\\bigg(\\overrightarrow{CB},\\overrightarrow{CD}\\bigg)$<\/span>&nbsp;= <span class=\"math-tex\">$\\dfrac{2\\sqrt{5}}{5}$<\/span>.<\/p><p>\u0110&aacute;p &aacute;n \u0111&uacute;ng l&agrave;&nbsp; <span style=\"color:#16a085;\">&nbsp;<strong>C.<\/strong> cos<span class=\"math-tex\">$\\bigg(\\overrightarrow{AB},\\overrightarrow{AD}\\bigg)$<\/span>&nbsp; = cos<span class=\"math-tex\">$\\bigg(\\overrightarrow{CB},\\overrightarrow{CD}\\bigg)$<\/span>.<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2023-06-01 02:17:29","option_type":"math","len":0},{"id":"7027","mon_id":"1158767","chapter_id":"1158890","post_id":"6459","question":"<p>Trong m\u1eb7t ph\u1eb3ng t\u1ecda \u0111\u1ed9 Oxy, cho hai vect\u01a1&nbsp;<span class=\"math-tex\">$\\overrightarrow{u}=2\\overrightarrow{i}+3\\overrightarrow{j}$<\/span>&nbsp; v&agrave;&nbsp;<span class=\"math-tex\">$\\overrightarrow{v}=m\\overrightarrow{i}-\\overrightarrow{j}$<\/span>&nbsp;.<\/p><p>T&igrave;m m \u0111\u1ec3&nbsp;<span class=\"math-tex\">$\\overrightarrow{u}$<\/span>&nbsp;vu&ocirc;ng g&oacute;c v\u1edbi&nbsp;<span class=\"math-tex\">$\\overrightarrow{v}$<\/span>&nbsp;.<\/p>","options":["<strong>A.<\/strong> m = 2","<strong>B.<\/strong> m = &ndash;2","<strong>C.<\/strong> m = <span class=\"math-tex\">$-\\dfrac{3}{2}$<\/span>","<strong>D.<\/strong> m = <span class=\"math-tex\">$\\dfrac{3}{2}$<\/span>"],"correct":"4","level":"2","hint":"","answer":"<p>Ta c&oacute;&nbsp;&nbsp;&nbsp;<span class=\"math-tex\">$\\overrightarrow{u}=2\\overrightarrow{i}+3\\overrightarrow{j}$<\/span>&nbsp; = (2; 3)&nbsp; v&agrave;&nbsp;<span class=\"math-tex\">$\\overrightarrow{v}=m\\overrightarrow{i}-\\overrightarrow{j}$<\/span>&nbsp;= (m;&nbsp;&ndash;1).<\/p><p>V&igrave;&nbsp;&nbsp;<span class=\"math-tex\">$\\overrightarrow{u} \\bot \\overrightarrow{v}$<\/span>&nbsp;n&ecirc;n&nbsp;<span class=\"math-tex\">$\\overrightarrow{u}.\\overrightarrow{v}$<\/span>&nbsp;= 0&nbsp;&hArr; 2m&nbsp;&ndash; 3 = 0&nbsp;&hArr; &nbsp;m =&nbsp;<span class=\"math-tex\">$\\dfrac{3}{2}$<\/span>&nbsp;.<\/p><p>\u0110&aacute;p &aacute;n \u0111&uacute;ng l&agrave;&nbsp; &nbsp;<span style=\"color:#16a085;\"><strong>D.<\/strong>&nbsp;m =&nbsp;<span class=\"math-tex\">$\\dfrac{3}{2}$<\/span>.<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2023-06-01 02:23:45","option_type":"math","len":0},{"id":"7029","mon_id":"1158767","chapter_id":"1158890","post_id":"6459","question":"<p>Trong m\u1eb7t ph\u1eb3ng t\u1ecda \u0111\u1ed9 Oxy, cho hai vect\u01a1&nbsp;<span class=\"math-tex\">$\\overrightarrow{u}=2\\overrightarrow{i}+3\\overrightarrow{j}$<\/span>&nbsp; v&agrave;&nbsp;<span class=\"math-tex\">$\\overrightarrow{v}=m\\overrightarrow{i}-\\overrightarrow{j}$<\/span>&nbsp;.<\/p><p>T&igrave;m m \u0111\u1ec3&nbsp;<span class=\"math-tex\">$\\overrightarrow{u}$<\/span>&nbsp;v&agrave;&nbsp;<span class=\"math-tex\">$\\overrightarrow{v}$<\/span>&nbsp; c&oacute; \u0111\u1ed9 d&agrave;i b\u1eb1ng nhau.<\/p>","options":["<strong>A.<\/strong> m = <span class=\"math-tex\">$\\pm 2\\sqrt{3}$<\/span>","<strong>B.<\/strong> m = <span class=\"math-tex\">$\\pm 3\\sqrt{2}$<\/span>","<strong>C.<\/strong> m =<span class=\"math-tex\">$\\pm \\sqrt{3}$<\/span>","<strong>D.<\/strong> m = <span class=\"math-tex\">$\\pm \\sqrt{2}$<\/span>"],"correct":"1","level":"2","hint":"","answer":"<p>Ta c&oacute;&nbsp;&nbsp;&nbsp;<span class=\"math-tex\">$\\overrightarrow{u}=2\\overrightarrow{i}+3\\overrightarrow{j}$<\/span>&nbsp; = (2; 3)&nbsp; v&agrave;&nbsp;<span class=\"math-tex\">$\\overrightarrow{v}=m\\overrightarrow{i}-\\overrightarrow{j}$<\/span>&nbsp;= (m;&nbsp;&ndash;1).<\/p><p><span class=\"math-tex\">$|\\overrightarrow{u}| = \\sqrt{2^2+3^2}=\\sqrt{13}$<\/span>&nbsp;;&nbsp;<span class=\"math-tex\">$|\\overrightarrow{v}|=\\sqrt{m^2+(-1)^2}=\\sqrt{m^2+1}$<\/span>&nbsp;.<\/p><p>V&igrave;&nbsp;&nbsp;<span class=\"math-tex\">$|\\overrightarrow{u}|=|\\overrightarrow{v}|$<\/span>&nbsp;n&ecirc;n&nbsp;<span class=\"math-tex\">$\\sqrt{13}=\\sqrt{m^2+1}$<\/span>&nbsp;= 0&nbsp;&hArr; 13 = m&sup2; + 1 &hArr; m&sup2; = 12&nbsp;&hArr;&nbsp;m =&nbsp;<span class=\"math-tex\">$\\pm 2\\sqrt{3}$<\/span>&nbsp;.<\/p><p>\u0110&aacute;p &aacute;n \u0111&uacute;ng l&agrave;&nbsp; <span style=\"color:#16a085;\">&nbsp;<strong>A.<\/strong> m =&nbsp;<span class=\"math-tex\">$\\pm 2\\sqrt{3}$<\/span>.<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2023-06-01 02:26:59","option_type":"math","len":0}]}