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Câu hỏi: Trong không gian Oxyz, cho hai vectơ $\vec{u}=\left( 1;0;2 \right)$ và $\vec{v}=\left( -1;2;0 \right).$ Tính $P=\cos \left( \vec{u};\vec{v} \right).$
A. $P=\dfrac{1}{25}.$
B. $P=\dfrac{1}{5}.$
C. $P=-\dfrac{1}{25}.$
D. $P=-\dfrac{1}{5}.$
A. $P=\dfrac{1}{25}.$
B. $P=\dfrac{1}{5}.$
C. $P=-\dfrac{1}{25}.$
D. $P=-\dfrac{1}{5}.$
Ta có $P=\cos \left( \vec{u};\vec{v} \right)=\dfrac{\vec{u}.\vec{v}}{\left| {\vec{u}} \right|.\left| {\vec{v}} \right|}=\dfrac{1.\left( -1 \right)+0.2+2.0}{\sqrt{{{1}^{2}}+{{0}^{2}}+{{2}^{2}}}.\sqrt{{{\left( -1 \right)}^{2}}+{{2}^{2}}+{{0}^{2}}}}=-\dfrac{1}{5}.$
Đáp án D.