Chú ý: Để đảm bảo quyền lợi và bảo vệ tài khoản của mình
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{"common":{"save":0,"post_id":"6456","level":1,"total":10,"point":10,"point_extra":0},"segment":[{"id":"6954","mon_id":"1158767","chapter_id":"1158890","post_id":"6456","question":"<p>Cho hai vect\u01a1 <span class=\"math-tex\">$\\overrightarrow{u}$<\/span> và <span class=\"math-tex\">$\\overrightarrow{v}$<\/span> cùng h\u01b0\u1edbng, khác vect\u01a1 <span class=\"math-tex\">$\\overrightarrow{0}$<\/span> . M\u1ec7nh \u0111\u1ec1 nào sau \u0111ây \u0111úng?<\/p>","options":["<strong>A.<\/strong> <span class=\"math-tex\">$\\overrightarrow{u}.\\overrightarrow{v}=|\\overrightarrow{u}|.|\\overrightarrow{v}|$<\/span>.","<strong>B.<\/strong> <span class=\"math-tex\">$\\overrightarrow{u}.\\overrightarrow{v}$<\/span> = 0.","<strong>C.<\/strong> <span class=\"math-tex\">$\\overrightarrow{u}.\\overrightarrow{v}$<\/span> = –1.","<strong>D.<\/strong> <span class=\"math-tex\">$\\overrightarrow{u}.\\overrightarrow{v}$<\/span> = 1."],"correct":"1","level":"1","hint":"","answer":"<p>Theo \u0111\u1ecbnh ngh\u0129a tích vô h\u01b0\u1edbng c\u1ee7a 2 vect\u01a1 ta có: <span class=\"math-tex\">$\\overrightarrow{u}.\\overrightarrow{v}=|\\overrightarrow{u}|.|\\overrightarrow{v}|.cos\\big(\u200b\u200b\\overrightarrow{u},\\overrightarrow{v}\\big)$<\/span>.<\/p><p>Vì <span class=\"math-tex\">$\\overrightarrow{u}$<\/span> và <span class=\"math-tex\">$\\overrightarrow{v}$<\/span> cùng h\u01b0\u1edbng nên <span class=\"math-tex\">$\\big(\\overrightarrow{u},\\overrightarrow{v}\\big) $<\/span> = 0° ⇒ cos<span class=\"math-tex\">$\\big(\\overrightarrow{u},\\overrightarrow{v}\\big)$<\/span> = 1.<\/p><p>V\u1eady <span class=\"math-tex\">$\\overrightarrow{u}.\\overrightarrow{v}=|\\overrightarrow{u}|.|\\overrightarrow{v}|$<\/span>.<\/p><p>\u0110áp án \u0111úng là <span style=\"color:#16a085;\"><strong>A.<\/strong> <span class=\"math-tex\">$\\overrightarrow{u}.\\overrightarrow{v}=|\\overrightarrow{u}|.|\\overrightarrow{v}|$<\/span>.<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2023-05-31 02:16:02","option_type":"math","len":0},{"id":"6955","mon_id":"1158767","chapter_id":"1158890","post_id":"6456","question":"<p>Cho hai vect\u01a1 <span class=\"math-tex\">$\\overrightarrow{u}$<\/span> và <span class=\"math-tex\">$\\overrightarrow{v}$<\/span> khác <span class=\"math-tex\">$\\overrightarrow{0}$<\/span>, <span class=\"math-tex\">$\\overrightarrow{u}.\\overrightarrow{v}=-|\\overrightarrow{u}|.|\\overrightarrow{v}|$<\/span>. G\u1ecdi a là góc gi\u1eefa hai vect\u01a1 <span class=\"math-tex\">$\\overrightarrow{u}$<\/span> và <span class=\"math-tex\">$\\overrightarrow{v}$<\/span>. Tính góc a.<\/p>","options":["<strong>A.<\/strong> a = 0°","<strong>B.<\/strong> a = 30°","<strong>C.<\/strong> a = 90°","<strong>D.<\/strong> a = 180°"],"correct":"4","level":"1","hint":"","answer":"<p>Theo \u0111\u1ecbnh ngh\u0129a tích vô h\u01b0\u1edbng c\u1ee7a 2 vect\u01a1 ta có: <span class=\"math-tex\">$\\overrightarrow{u}.\\overrightarrow{v}=|\\overrightarrow{u}|.|\\overrightarrow{v}|.cos\\big(\u200b\u200b\\overrightarrow{u},\\overrightarrow{v}\\big)$<\/span>.<\/p><p>Vì <span class=\"math-tex\">$\\overrightarrow{u}.\\overrightarrow{v}=-|\\overrightarrow{u}|.|\\overrightarrow{v}|$<\/span> nên cos<span class=\"math-tex\">$\\big(\\overrightarrow{u},\\overrightarrow{v}\\big)$<\/span> = –1 ⇒ <span class=\"math-tex\">$\\big(\\overrightarrow{u},\\overrightarrow{v}\\big) $<\/span> = 180°.<\/p><p>\u0110áp án \u0111úng là <span style=\"color:#16a085;\"><strong>D.<\/strong> a = 180°.<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2023-05-31 02:19:22","option_type":"txt","len":1},{"id":"6957","mon_id":"1158767","chapter_id":"1158890","post_id":"6456","question":"<p>Cho hai vect\u01a1 <span class=\"math-tex\">$\\overrightarrow{u}$<\/span> và <span class=\"math-tex\">$\\overrightarrow{v}$<\/span> th\u1ecfa mãn <span class=\"math-tex\">$|\\overrightarrow{u}|$<\/span> = 5 , <span class=\"math-tex\">$|\\overrightarrow{v}|$<\/span> = 2 và <span class=\"math-tex\">$\\overrightarrow{u}.\\overrightarrow{v}$<\/span> = 5. Tính s\u1ed1 \u0111o c\u1ee7a góc gi\u1eefa hai vect\u01a1 <span class=\"math-tex\">$\\overrightarrow{u}$<\/span> và <span class=\"math-tex\">$\\overrightarrow{v}$<\/span>.<\/p>","options":["<strong>A.<\/strong> 30°","<strong>B.<\/strong> 45°","<strong>C. <\/strong>60°","<strong>D.<\/strong> 90°"],"correct":"3","level":"1","hint":"","answer":"<p>Theo \u0111\u1ecbnh ngh\u0129a tích vô h\u01b0\u1edbng c\u1ee7a 2 vect\u01a1 ta có: <span class=\"math-tex\">$\\overrightarrow{u}.\\overrightarrow{v}=|\\overrightarrow{u}|.|\\overrightarrow{v}|.cos\\big(\u200b\u200b\\overrightarrow{u},\\overrightarrow{v}\\big)$<\/span>.<\/p><p>⇒ cos<span class=\"math-tex\">$\\big(\\overrightarrow{u},\\overrightarrow{v}\\big)$<\/span> = <span class=\"math-tex\">$\\dfrac{\\overrightarrow{u}.\\overrightarrow{v}}{|\\overrightarrow{u}|.|\\overrightarrow{v}|}$<\/span> = <span class=\"math-tex\">$\\dfrac{5}{5.2}$<\/span> = <span class=\"math-tex\">$\\dfrac{1}{2}$<\/span> ⇒ <span class=\"math-tex\">$\\big(\\overrightarrow{u},\\overrightarrow{v}\\big) $<\/span> = 60°.<\/p><p>\u0110áp án \u0111úng là <span style=\"color:#16a085;\"><strong>C. <\/strong>60°.<\/span><\/p>","type":"choose","extra_type":"classic","user_id":"131","test":"0","date":"2023-05-31 02:24:26","option_type":"txt","len":0}]}