{"common":{"save":0,"post_id":"7592","level":2,"total":10,"point":10,"point_extra":0},"segment":[{"id":"5645","post_id":"7592","mon_id":"1159285","chapter_id":"1159392","question":"<p>Trong kh&ocirc;ng gian Oxyz, cho&nbsp;<span class=\"math-tex\">$\\overrightarrow{a}=(-2;2;0),\\overrightarrow{b}=(2;2;0),\\overrightarrow{c}=(2;2;2)$<\/span>. Gi&aacute; tr\u1ecb c\u1ee7a&nbsp;<span class=\"math-tex\">$|\\overrightarrow{a}+\\overrightarrow{b}+\\overrightarrow{c}|$<\/span>&nbsp;b\u1eb1ng<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$\\sqrt{6}$<\/span>","<strong>B.<\/strong> <span class=\"math-tex\">$\\sqrt{11}$<\/span>","<strong>C.<\/strong> <span class=\"math-tex\">$2\\sqrt{11}$<\/span>","<strong>D.<\/strong> <span class=\"math-tex\">$2\\sqrt{6}$<\/span>"],"correct":"3","level":"2","hint":"","answer":"<p>Ch\u1ecdn&nbsp;<span style=\"color:#16a085;\"><strong>C.<\/strong>&nbsp;<span class=\"math-tex\">$2\\sqrt{11}$<\/span>.<\/span><\/p><p><span class=\"math-tex\">$\\overrightarrow{a}+\\overrightarrow{b}+\\overrightarrow{c}=(2;6;2)$<\/span>&nbsp;&rArr;&nbsp;<span class=\"math-tex\">$|\\overrightarrow{a}+\\overrightarrow{b}+\\overrightarrow{c}|=\\sqrt{2^2+6^2+2^2}=2\\sqrt{11}$<\/span>.<\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-09-02 03:47:22","option_type":"math","len":0},{"id":"5646","post_id":"7592","mon_id":"1159285","chapter_id":"1159392","question":"<p>Trong kh&ocirc;ng gian v\u1edbi h\u1ec7 tr\u1ee5c t\u1ecda \u0111\u1ed9 Oxyz, cho hai vect\u01a1&nbsp;<span class=\"math-tex\">$\\overrightarrow{a}=(2;1;0),\\overrightarrow{b}=(-1;0;-2)$<\/span>. T&iacute;nh&nbsp;<span class=\"math-tex\">$\\cos (\\overrightarrow{a},\\overrightarrow{b})$<\/span>.<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$-\\dfrac{2}{25}$<\/span>","<strong>B.<\/strong> <span class=\"math-tex\">$-\\dfrac{2}{5}$<\/span>","<strong>C.<\/strong> <span class=\"math-tex\">$\\dfrac{2}{25}$<\/span>","<strong>D.<\/strong> <span class=\"math-tex\">$\\dfrac{2}{5}$<\/span>"],"correct":"2","level":"2","hint":"","answer":"<p>Ch\u1ecdn&nbsp;<span style=\"color:#16a085;\"><strong>B.<\/strong>&nbsp;<span class=\"math-tex\">$-\\dfrac{2}{5}$<\/span>.<\/span><\/p><p><span class=\"math-tex\">$\\cos (\\overrightarrow{a},\\overrightarrow{b})=\\dfrac{\\overrightarrow{a}.\\overrightarrow{b}}{|\\overrightarrow{a}|.|\\overrightarrow{b}|}=\\dfrac{-2}{\\sqrt{5}.\\sqrt{5}}=-\\dfrac{2}{5}$<\/span>.<\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-09-02 03:54:41","option_type":"math","len":0},{"id":"5648","post_id":"7592","mon_id":"1159285","chapter_id":"1159392","question":"<p>Tr&ecirc;n m\u1eb7t ph\u1eb3ng to\u1ea1 \u0111\u1ed9 Oxyz, cho tam gi&aacute;c ABC&nbsp;bi\u1ebft <span class=\"math-tex\">$A(1;3;0)$<\/span>,&nbsp;<span class=\"math-tex\">$B(-2;-2;0)$<\/span>,&nbsp;<span class=\"math-tex\">$C(3;1;0)$<\/span>. T&iacute;nh cosin g&oacute;c&nbsp;A c\u1ee7a tam gi&aacute;c.<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$\\dfrac{2}{\\sqrt{17}}$<\/span>","<strong>B.<\/strong> <span class=\"math-tex\">$\\dfrac{1}{\\sqrt{17}}$<\/span>","<strong>C.<\/strong> <span class=\"math-tex\">$-\\dfrac{2}{\\sqrt{17}}$<\/span>","<strong>D.<\/strong> <span class=\"math-tex\">$-\\dfrac{1}{\\sqrt{17}}$<\/span>"],"correct":"2","level":"2","hint":"","answer":"<p>Ch\u1ecdn&nbsp;<span style=\"color:#16a085;\"><strong>B.<\/strong>&nbsp;<span class=\"math-tex\">$\\dfrac{1}{\\sqrt{17}}$<\/span>.<\/span><\/p><p>Ta c&oacute;&nbsp;<span class=\"math-tex\">$\\overrightarrow{AB}=(-3;-5;0),\\overrightarrow{AC}=(2;-2;0)$<\/span><\/p><p>Khi \u0111&oacute;&nbsp;<span class=\"math-tex\">$\\cos A=\\cos (\\overrightarrow{AB},\\overrightarrow{AC})=\\dfrac{\\overrightarrow{AB}.\\overrightarrow{AC}}{AB.AC}=\\dfrac{-3.2+5.2+0.0}{\\sqrt{34}.2\\sqrt{2}}=\\dfrac{1}{\\sqrt{17}}$<\/span>.<\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-09-02 04:04:39","option_type":"math","len":0}]}