{"save":1,"level":1,"time":"45","total":20,"point":5,"segment":[{"id":"588","test_id":"266","question":"<p>Trong kh&ocirc;ng gian Oxyz cho hai vect\u01a1 <span class=\"math-tex\">$\\overrightarrow{a}=(a_{1}^{{}};a_{2}^{{}};a_{3}^{{}}),\\overset{{}}{\\mathop{{}}}\\,\\overrightarrow{b}=(b_{1}^{{}};b_{2}^{{}};b_{3}^{{}})$<\/span>&nbsp; \u0111\u1ec1u kh&aacute;c vect\u01a1-kh&ocirc;ng.<\/p><p>G\u1ecdi &alpha; l&agrave; g&oacute;c gi\u1eefa hai vect\u01a1 <span class=\"math-tex\">$\\overrightarrow{a}, \\overrightarrow{b}$<\/span>.&nbsp; C&acirc;u n&agrave;o sai trong c&aacute;c c&acirc;u sau:<br \/>&nbsp;<\/p>","options":["<span class=\"math-tex\">$\\overrightarrow{a}\\bot \\overrightarrow{b}\\Leftrightarrow {{a}_{1}}{{b}_{1}}+{{a}_{2}}{{b}_{2}}+{{a}_{3}}{{b}_{3}}=0$<\/span>","<span class=\"math-tex\">$\\cos \\alpha =\\frac{{{a}_{1}}{{b}_{1}}+{{a}_{2}}{{b}_{2}}+{{a}_{3}}{{b}_{3}}}{({{a}_{1}}^{2}+{{a}_{2}}^{2}+{{a}_{3}}^{2}).({{b}_{1}}^{2}+{{b}_{2}}^{2}+{{b}_{3}}^{2})}$<\/span>","<span class=\"math-tex\">$\\cos \\alpha =\\frac{\\overrightarrow{a}.\\overrightarrow{b}}{\\left| \\overrightarrow{a} \\right|.\\left| \\overrightarrow{b} \\right|}.\u00a0\u00a0 \u00a0$<\/span>","<span class=\"math-tex\">$\\cos \\alpha =\\frac{{{a}_{1}}{{b}_{1}}+{{a}_{2}}{{b}_{2}}+{{a}_{3}}{{b}_{3}}}{\\sqrt{{{a}_{1}}^{2}+{{a}_{2}}^{2}+{{a}_{3}}^{2}}.\\sqrt{{{b}_{1}}^{2}+{{b}_{2}}^{2}+{{b}_{3}}^{2}}}$<\/span>"],"correct":"2","answer":"<p><span class=\"math-tex\">$\\cos \\alpha =\\frac{{{a}_{1}}{{b}_{1}}+{{a}_{2}}{{b}_{2}}+{{a}_{3}}{{b}_{3}}}{\\sqrt{{{a}_{1}}^{2}+{{a}_{2}}^{2}+{{a}_{3}}^{2}}.\\sqrt{{{b}_{1}}^{2}+{{b}_{2}}^{2}+{{b}_{3}}^{2}}}$<\/span><\/p>","type":"choose","user_id":"108","test":"0","date":"2020-03-20 23:17:18"},{"id":"589","test_id":"266","question":"<p>Trong kh&ocirc;ng gian Oxyz, cho hai \u0111i\u1ec3m <span class=\"math-tex\">$A\\left( 1;\\,1;\\,-2 \\right)$<\/span> v&agrave; <span class=\"math-tex\">$B\\left( 2;\\,2;\\,1 \\right)$<\/span>.<\/p><p>Vect\u01a1 <span class=\"math-tex\">$\\overrightarrow{AB}$<\/span> c&oacute; t\u1ecda \u0111\u1ed9 l&agrave;:<br \/>&nbsp;<\/p>","options":["<span class=\"math-tex\">$\\left( 3;\\,3;\\,-1 \\right)$<\/span>","<span class=\"math-tex\">$\\left( 3;\\,1;\\,1 \\right)$<\/span>","<span class=\"math-tex\">$\\left( -1;\\,-1;\\,-3 \\right)$<\/span>","<span class=\"math-tex\">$\\left( 1;\\,1;\\,3 \\right)$<\/span>"],"correct":"4","answer":"<p><span class=\"math-tex\">$A\\left( 1;\\,1;\\,-2 \\right), B(2;2;1)$<\/span><\/p><p><span class=\"math-tex\">$\\overrightarrow{AB}=(2-1;2-1;1+2)=(1;1;3)$<\/span><\/p>","type":"choose","user_id":"108","test":"0","date":"2020-03-20 23:22:24"}]}