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  • The angle between two vectors vector a and vector b with magnitudes root3 and 4, respectively, and vector a . vector b = 2root3 is A. pi/6

The angle between two vectors \vec{a}  and \vec{b}  with magnitudes \sqrt3  and 4, respectively, and \vec{a}.\vec{b}=2\sqrt3  is

\\A. \frac{\pi}{6}\\\\ B.\frac{\pi}{3}\\\\ C. \frac{\pi}{2} \\\\ D. \frac{5\pi}{2}

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Answer :(B)

Given that,  |\vec{\mathrm{a}}|=\sqrt{3},|\vec{\mathrm{b}}|=4 \text { and } \vec{\mathrm{a}} \cdot \vec{\mathrm{b}}=2 \sqrt{3}

Let θ be the angle between vector a and b.

\\ \text { Then, } \vec{\mathrm{a}} \cdot \vec{\mathrm{b}}=|\vec{\mathrm{a}}||\vec{\mathrm{b}}| \cos \theta \\ \Rightarrow 2 \sqrt{3}=\sqrt{3} .4 \cos \theta \\ \Rightarrow \quad \cos \theta=\frac{2 \sqrt{3}}{\sqrt{3} .4}=\frac{1}{2} \\ \Rightarrow \theta=\frac{\pi}{3}

 

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infoexpert22

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