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Giải bài tập 6 trang 65 SGK Toán 12 tập 1 - Chân trời sáng tạo

Gọi a là góc giữa hai vectơ \(\overrightarrow u = (0; - 1;0)\) và \(\overrightarrow v = (\sqrt 3 ;1;0)\). Giá trị của \(\alpha \) là A. \(\alpha = \frac{\pi }{6}\). B. \(\alpha = \frac{\pi }{3}\). C. \(\alpha = \frac{{2\pi }}{3}\). D. \(\alpha = \frac{\pi }{2}\).

ꩲTổng hợp đề thi học kì 2 lớp 12 tất cả các môn - Chân trời sáng tạo

Toán - Văn - Anh - Hoá - Sinh - Sử - Địa
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Đề bài

 
 
Gọi a là góc giữa hai vectơ \(\overrightarrow u  = (0; - 1;0)\) và \(\overrightarrow v  = (\sqrt 3 ;1;0)\). Giá trị của \(\alpha \) là A. \(\alpha  = \frac{\pi }{6}\). B. \(\alpha  = \frac{\pi }{3}\). C. \(\alpha  = \frac{{2\pi }}{3}\). D. \(\alpha  = \frac{\pi }{2}\).
 

Phương pháp giải - Xem chi tiết

Ta có: \(\cos (\overrightarrow a ,\overrightarrow b ) = \frac{{\overrightarrow a .\overrightarrow b }}{{|\overrightarrow a |.|\overrightarrow b |}}\)

 

Lời giải chi tiết

Chọn C \(\cos (\overrightarrow u ,\overrightarrow v ) = \frac{{\overrightarrow u .\overrightarrow v }}{{|\overrightarrow u |.|\overrightarrow v |}} = \frac{{0.\sqrt 3  - 1.1 + 0.0}}{{\sqrt {{1^2}} .\sqrt {{{(\sqrt 3 )}^2} + {1^2}} }} =  - \frac{1}{2} \Rightarrow (\overrightarrow u ,\overrightarrow v ) = \frac{{2\pi }}{3}\)
 

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