{"common":{"save":0,"post_id":"6514","level":1,"total":10,"point":10,"point_extra":0},"segment":[{"id":"7202","mon_id":"1158767","chapter_id":"1158915","post_id":"6514","question":"<p>Kh\u1eb3ng \u0111\u1ecbnh n&agrave;o <strong>sai<\/strong>?<\/p>","options":["<strong>A. <span class=\"math-tex\">$1.\\overrightarrow{a}=\\overrightarrow{a}$<\/span><\/strong>.","<strong>B. <span class=\"math-tex\">$k.\\overrightarrow{a}$<\/span><\/strong> v&agrave; <strong><span class=\"math-tex\">$\\overrightarrow{a}$<\/span><\/strong> c&ugrave;ng h\u01b0\u1edbng khi k &gt; 0.","<strong>C. <span class=\"math-tex\">$k.\\overrightarrow{a}$<\/span><\/strong> v&agrave; <strong><span class=\"math-tex\">$\\overrightarrow{a}$<\/span><\/strong> c&ugrave;ng h\u01b0\u1edbng khi k &lt; 0.","<strong>D. <\/strong>Hai vect\u01a1 <span class=\"math-tex\">$\\overrightarrow{a}$<\/span> v&agrave; <span class=\"math-tex\">$\\overrightarrow{b}\\ne\\overrightarrow{0}$<\/span> c&ugrave;ng ph\u01b0\u01a1ng khi c&oacute; m\u1ed9t s\u1ed1 k \u0111\u1ec3 <span class=\"math-tex\">$\\overrightarrow{a}=k.\\overrightarrow{b}$<\/span>"],"correct":"3","level":"1","hint":"","answer":"<p>Ch\u1ecdn <span style=\"color:#16a085;\"><\/span><span style=\"color:#16a085;\"><strong>C.&nbsp;<span class=\"math-tex\">$k.\\overrightarrow{a}$<\/span><\/strong>&nbsp;v&agrave;&nbsp;<strong><span class=\"math-tex\">$\\overrightarrow{a}$<\/span><\/strong>&nbsp;c&ugrave;ng h\u01b0\u1edbng khi k &lt;&nbsp;0.<\/span><span style=\"color:#16a085;\"> <\/span><\/p><p><span style=\"color:#16a085;\"><\/span>(Theo \u0111\u1ecbnh ngh\u0129a t&iacute;ch c\u1ee7a m\u1ed9t s\u1ed1 v\u1edbi m\u1ed9t vect\u01a1).<\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2023-06-21 07:10:10","option_type":"math","len":0},{"id":"7203","mon_id":"1158767","chapter_id":"1158915","post_id":"6514","question":"<p>T&igrave;m gi&aacute; tr\u1ecb c\u1ee7a m sao cho <span class=\"math-tex\">$\\overrightarrow{a}=m.\\overrightarrow{b}$<\/span>, bi\u1ebft r\u1eb1ng&nbsp;<span class=\"math-tex\">$\\overrightarrow{a},\\overrightarrow{b}$<\/span> ng\u01b0\u1ee3c h\u01b0\u1edbng <span class=\"math-tex\">$|\\overrightarrow{a}|=5$<\/span>v&agrave; <span class=\"math-tex\">$|\\overrightarrow{b}|=15$<\/span>.&nbsp;<\/p>","options":["<strong>A. <span class=\"math-tex\">$m=3$<\/span><\/strong>","<strong>B. <span class=\"math-tex\">$m=-\\dfrac{1}{3}$<\/span><\/strong>","<strong>C. <span class=\"math-tex\">$m=\\dfrac{1}{3}$<\/span><\/strong>","<strong>D. <span class=\"math-tex\">$m=-3$<\/span><\/strong>"],"correct":"2","level":"1","hint":"","answer":"<p>V&igrave;&nbsp;<span class=\"math-tex\">$\\overrightarrow{a},\\overrightarrow{b}$<\/span>&nbsp;ng\u01b0\u1ee3c h\u01b0\u1edbng n&ecirc;n&nbsp;<span class=\"math-tex\">$m=-\\dfrac{|\\overrightarrow{a}|}{|\\overrightarrow{b}|}=-\\dfrac{5}{15}=-\\dfrac{1}{3}$<\/span><\/p><p>Ch\u1ecdn&nbsp;<span style=\"color:#16a085;\"><strong>B.&nbsp;<span class=\"math-tex\">$m=-\\dfrac{1}{3}$<\/span><\/strong><\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2023-06-21 07:23:30","option_type":"math","len":0},{"id":"7204","mon_id":"1158767","chapter_id":"1158915","post_id":"6514","question":"<p>Cho tam gi&aacute;c OAB vu&ocirc;ng c&acirc;n t\u1ea1i O v\u1edbi OA = OB = a. \u0110\u1ed9 d&agrave;i c\u1ee7a vect\u01a1&nbsp;<span class=\"math-tex\">$\\overrightarrow{n}=\\dfrac{21}{4}\\overrightarrow{OA}-\\dfrac{5}{2}\\overrightarrow{OB}$<\/span> l&agrave;:<\/p>","options":["<strong>A. <span class=\"math-tex\">$\\dfrac{a\\sqrt{140}}{4}$<\/span><\/strong>","<strong>B. <span class=\"math-tex\">$\\dfrac{a\\sqrt{321}}{4}$<\/span><\/strong>","<strong>C. <span class=\"math-tex\">$\\dfrac{a\\sqrt{520}}{4}$<\/span><\/strong>","<strong>D. <span class=\"math-tex\">$\\dfrac{a\\sqrt{541}}{4}$<\/span><\/strong>"],"correct":"4","level":"1","hint":"","answer":"<p><span 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y=\"7.5\"><\/image> <\/g> <\/svg><\/span><\/p><p>D\u1ef1ng \u0111i\u1ec3m M, N sao cho&nbsp;<span class=\"math-tex\">$\\overrightarrow{OM}=\\dfrac{21}{4}\\overrightarrow{OA}$<\/span>&nbsp;v&agrave; <span class=\"math-tex\">$\\overrightarrow{ON}=\\dfrac{5}{2}\\overrightarrow{OB}$<\/span>. Khi \u0111&oacute;:<\/p><p><span class=\"math-tex\">$|\\overrightarrow{n}|=|\\overrightarrow{OM}-\\overrightarrow{ON}|=|\\overrightarrow{NM}|=MN=\\sqrt{OM^2+ON^2}$<\/span><\/p><p><span class=\"math-tex\">$= \\sqrt{\\bigg(\\dfrac{21a}{4}\\bigg)^2+\\bigg(\\dfrac{5a}{2}\\bigg)^2}$<\/span><strong>&nbsp;<span class=\"math-tex\">$=\\dfrac{a\\sqrt{541}}{4}$<\/span><\/strong><\/p><p>Ch\u1ecdn&nbsp;<span style=\"color:#16a085;\"><strong>D.&nbsp;<span class=\"math-tex\">$\\dfrac{a\\sqrt{541}}{4}$<\/span><\/strong><\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2023-06-21 07:39:39","option_type":"math","len":0}]}