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Câu hỏi: Gọi $\left( \alpha \right)$ là góc giữa hai vectơ $\overrightarrow{u}=\left( 2; 1 ; -2 \right)$ ; $\overrightarrow{v}=\left( -3 ; 4 ; 0 \right)$. Tính $cos\alpha $
A. $\dfrac{2}{15}$.
B. $\dfrac{2}{\sqrt{15}}$.
C. $-\dfrac{2}{\sqrt{15}}$.
D. $-\dfrac{2}{15}$.
A. $\dfrac{2}{15}$.
B. $\dfrac{2}{\sqrt{15}}$.
C. $-\dfrac{2}{\sqrt{15}}$.
D. $-\dfrac{2}{15}$.
Ta có $cos\alpha =\dfrac{\overrightarrow{u}.\overrightarrow{v}}{\left| \overrightarrow{u} \right|.\left| \overrightarrow{v} \right|}=\dfrac{2.\left( -3 \right)+1.4+\left( -2 \right).0}{\sqrt{{{2}^{2}}+{{1}^{2}}+{{\left( -2 \right)}^{2}}}.\sqrt{{{\left( -3 \right)}^{2}}+{{4}^{2}}+{{0}^{2}}}}=-\dfrac{2}{15}$.
Đáp án D.