{"common":{"save":0,"post_id":"7306","level":2,"total":10,"point":10,"point_extra":0},"segment":[{"id":"7545","mon_id":"1158767","chapter_id":"1159256","post_id":"7306","question":"<p>Trong m\u1eb7t ph\u1eb3ng t\u1ecda \u0111\u1ed9 Oxy, cho hai vect\u01a1 <span class=\"math-tex\">$A(1;2)$<\/span>, <span class=\"math-tex\">$B(-1;1)$<\/span> và <span class=\"math-tex\">$C(5;-1)$<\/span>. Tính cosin c\u1ee7a góc gi\u1eefa hai vect\u01a1 <span class=\"math-tex\">$\\overrightarrow{AB}$<\/span> và <span class=\"math-tex\">$\\overrightarrow{AC}$<\/span>.<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$-\\dfrac{1}{2}$<\/span>","<strong>B.<\/strong> <span class=\"math-tex\">$\\dfrac{\\sqrt{3}}{2}$<\/span>","C. <span class=\"math-tex\">$-\\dfrac{2}{5}$<\/span>","<strong>D.<\/strong> <span class=\"math-tex\">$-\\dfrac{\\sqrt{5}}{5}$<\/span>"],"correct":"4","level":"2","hint":"","answer":"<p>\u0110\u1eb7t <span class=\"math-tex\">$\\overrightarrow{a}=\\overrightarrow{AB}=(-2;-1)$<\/span> ; <span class=\"math-tex\">$\\overrightarrow{b}=\\overrightarrow{AC}=(4;-3)$<\/span>.<\/p><p><span class=\"math-tex\">$\\cos(\\overrightarrow{a};\\overrightarrow{b}) =\\dfrac{\\overrightarrow{a}.\\overrightarrow{b}}{|\\overrightarrow{a}|.|\\overrightarrow{b}|} =\\dfrac{-2.4+1.3}{\\sqrt{2^2+1^2}.\\sqrt{4^2+3^2}}=-\\dfrac{\\sqrt{5}}{5}$<\/span>.<\/p><p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>D.<\/strong> <span class=\"math-tex\">$-\\dfrac{\\sqrt{5}}{5}$<\/span>.<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-04-14 06:18:00","option_type":"math","len":0},{"id":"7548","mon_id":"1158767","chapter_id":"1159256","post_id":"7306","question":"<p>Trong m\u1eb7t ph\u1eb3ng t\u1ecda \u0111\u1ed9 Oxy, cho vect\u01a1 <span class=\"math-tex\">$\\overrightarrow{a}=(9;3)$<\/span>. Vect\u01a1 nào sau \u0111ây <strong>không<\/strong> vuông góc v\u1edbi <span class=\"math-tex\">$\\overrightarrow{a}$<\/span> ?<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$\\overrightarrow{v_1}=(1;-3)$<\/span>","<strong>B.<\/strong> <span class=\"math-tex\">$\\overrightarrow{v_2}=(2;-6)$<\/span>","<strong>C.<\/strong> <span class=\"math-tex\">$\\overrightarrow{v_3}=(1;3)$<\/span>","<strong>D.<\/strong> <span class=\"math-tex\">$\\overrightarrow{v_4}=(-1;3)$<\/span>"],"correct":"3","level":"2","hint":"","answer":"<p>Ki\u1ec3m tra tích vô h\u01b0\u1edbng c\u1ee7a <span class=\"math-tex\">$\\overrightarrow{a}$<\/span> và vect\u01a1 \u0111ó, tích vô h\u01b0\u1edbng nào khác 0 thì vect\u01a1 \u0111ó không vuông góc v\u1edbi <span class=\"math-tex\">$\\overrightarrow{a}$<\/span>.<\/p><p>Ta có <span class=\"math-tex\">$\\overrightarrow{a}.\\overrightarrow{v_3}=9.1+3.3=18 \\ne0$<\/span> nên <span class=\"math-tex\">$\\overrightarrow{v_3}$<\/span> không vuông góc v\u1edbi <span class=\"math-tex\">$\\overrightarrow{a}$<\/span>.<\/p><p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>C.<\/strong> <span class=\"math-tex\">$\\overrightarrow{v_3}=(1;3)$<\/span>.<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-04-14 06:30:34","option_type":"math","len":0},{"id":"7549","mon_id":"1158767","chapter_id":"1159256","post_id":"7306","question":"<p>Trong m\u1eb7t ph\u1eb3ng t\u1ecda \u0111\u1ed9 Oxy, cho tam giác ABC có <span class=\"math-tex\">$A(6;0),B(3;1),C(-1;-1)$<\/span>. Tính s\u1ed1 \u0111o góc B c\u1ee7a tam giác \u0111ã cho.<\/p>","options":["<strong>A.<\/strong> 15°","<strong>B.<\/strong> 45°","<strong>C.<\/strong> 120°","<strong>D.<\/strong> 135°"],"correct":"4","level":"2","hint":"","answer":"<p>Ta có <span class=\"math-tex\">$\\overrightarrow{BA}=(3;-1);\\overrightarrow{BC}=(-4;-2)$<\/span>.<\/p><p>Suy ra <span class=\"math-tex\">$\\cos(\\overrightarrow{BA},\\overrightarrow{BC})=\\dfrac{\\overrightarrow{BA}.\\overrightarrow{BC}}{|\\overrightarrow{BA}|.|\\overrightarrow{BC}|}$<\/span> <span class=\"math-tex\">$=\\dfrac{-3.4+1.2}{\\sqrt{9+1}.\\sqrt{16+4}}=-\\dfrac{\\sqrt{2}}{2}$<\/span> .<\/p><p>Suy ra <span class=\"math-tex\">$\\widehat{B}=\\bigg(\\overrightarrow{BA},\\overrightarrow{BC}\\bigg)=135^0$<\/span>.<\/p><p>Ch\u1ecdn <span style=\"color:#16a085;\"><strong>D.<\/strong> 135°.<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2024-04-14 06:39:34","option_type":"txt","len":1}]}