Chú ý: Để đảm bảo quyền lợi và bảo vệ tài khoản của mình
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{"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(–2; –5), B(6; –1), C(3; –10) và D(8; –5).<\/p><p>Kh\u1eb3ng \u0111\u1ecbnh nào sau \u0111ây là <strong>\u0111úng<\/strong>?<\/p>","options":["<strong>A.<\/strong> Góc BAD và góc BCD ph\u1ee5 nhau.","<strong>B.<\/strong> Góc BCD là góc tù.","<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> Góc BAD và góc BCD bù nhau."],"correct":"3","level":"2","hint":"","answer":"<p>Ta có <span class=\"math-tex\">$\\overrightarrow{AB}$<\/span> = (8; 4) ; <span class=\"math-tex\">$\\overrightarrow{AD}$<\/span> = (10; 0) ; <span class=\"math-tex\">$\\overrightarrow{CB}$<\/span> = (3; 9) ; <span class=\"math-tex\">$\\overrightarrow{CD}$<\/span> = (5; 5) .<\/p><p>cos<span class=\"math-tex\">$\\bigg(\\overrightarrow{AB},\\overrightarrow{AD}\\bigg)$<\/span> = <span class=\"math-tex\">$\\dfrac{\\overrightarrow{AB},\\overrightarrow{AD}}{|\\overrightarrow{AB}|.|\\overrightarrow{AD}|}$<\/span> = <span class=\"math-tex\">$\\dfrac{8.10+4.0}{\\sqrt{8^2+4^2}.\\sqrt{10^2+0^2}}$<\/span> = <span class=\"math-tex\">$\\dfrac{2\\sqrt{5}}{5}$<\/span> .<\/p><p>cos<span class=\"math-tex\">$\\bigg(\\overrightarrow{CB},\\overrightarrow{CD}\\bigg)$<\/span>= <span class=\"math-tex\">$\\dfrac{\\overrightarrow{CB},\\overrightarrow{CD}}{|\\overrightarrow{CB}|.|\\overrightarrow{CD}|}$<\/span> = <span class=\"math-tex\">$\\dfrac{3.5+9.5}{\\sqrt{3^2+9^2}.\\sqrt{5^2+5^2}}$<\/span> = <span class=\"math-tex\">$\\dfrac{2\\sqrt{5}}{5}$<\/span> .<\/p><p>Suy ra cos<span class=\"math-tex\">$\\bigg(\\overrightarrow{AB},\\overrightarrow{AD}\\bigg)$<\/span> = cos<span class=\"math-tex\">$\\bigg(\\overrightarrow{CB},\\overrightarrow{CD}\\bigg)$<\/span> = <span class=\"math-tex\">$\\dfrac{2\\sqrt{5}}{5}$<\/span>.<\/p><p>\u0110áp án \u0111úng là <span style=\"color:#16a085;\"> <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>.<\/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 <span class=\"math-tex\">$\\overrightarrow{u}=2\\overrightarrow{i}+3\\overrightarrow{j}$<\/span> và <span class=\"math-tex\">$\\overrightarrow{v}=m\\overrightarrow{i}-\\overrightarrow{j}$<\/span> .<\/p><p>Tìm m \u0111\u1ec3 <span class=\"math-tex\">$\\overrightarrow{u}$<\/span> vuông góc v\u1edbi <span class=\"math-tex\">$\\overrightarrow{v}$<\/span> .<\/p>","options":["<strong>A.<\/strong> m = 2","<strong>B.<\/strong> m = –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 có <span class=\"math-tex\">$\\overrightarrow{u}=2\\overrightarrow{i}+3\\overrightarrow{j}$<\/span> = (2; 3) và <span class=\"math-tex\">$\\overrightarrow{v}=m\\overrightarrow{i}-\\overrightarrow{j}$<\/span> = (m; –1).<\/p><p>Vì <span class=\"math-tex\">$\\overrightarrow{u} \\bot \\overrightarrow{v}$<\/span> nên <span class=\"math-tex\">$\\overrightarrow{u}.\\overrightarrow{v}$<\/span> = 0 ⇔ 2m – 3 = 0 ⇔ m = <span class=\"math-tex\">$\\dfrac{3}{2}$<\/span> .<\/p><p>\u0110áp án \u0111úng là <span style=\"color:#16a085;\"><strong>D.<\/strong> m = <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 <span class=\"math-tex\">$\\overrightarrow{u}=2\\overrightarrow{i}+3\\overrightarrow{j}$<\/span> và <span class=\"math-tex\">$\\overrightarrow{v}=m\\overrightarrow{i}-\\overrightarrow{j}$<\/span> .<\/p><p>Tìm m \u0111\u1ec3 <span class=\"math-tex\">$\\overrightarrow{u}$<\/span> và <span class=\"math-tex\">$\\overrightarrow{v}$<\/span> có \u0111\u1ed9 dài 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 có <span class=\"math-tex\">$\\overrightarrow{u}=2\\overrightarrow{i}+3\\overrightarrow{j}$<\/span> = (2; 3) và <span class=\"math-tex\">$\\overrightarrow{v}=m\\overrightarrow{i}-\\overrightarrow{j}$<\/span> = (m; –1).<\/p><p><span class=\"math-tex\">$|\\overrightarrow{u}| = \\sqrt{2^2+3^2}=\\sqrt{13}$<\/span> ; <span class=\"math-tex\">$|\\overrightarrow{v}|=\\sqrt{m^2+(-1)^2}=\\sqrt{m^2+1}$<\/span> .<\/p><p>Vì <span class=\"math-tex\">$|\\overrightarrow{u}|=|\\overrightarrow{v}|$<\/span> nên <span class=\"math-tex\">$\\sqrt{13}=\\sqrt{m^2+1}$<\/span> = 0 ⇔ 13 = m² + 1 ⇔ m² = 12 ⇔ m = <span class=\"math-tex\">$\\pm 2\\sqrt{3}$<\/span> .<\/p><p>\u0110áp án \u0111úng là <span style=\"color:#16a085;\"> <strong>A.<\/strong> m = <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}]}