Find the angle between the two vectors \vec{a} \,and \, \vec{b} with magnitude 2 and \sqrt{3} respectively and \vec{a.} \, \vec{b}=4.

(a) \frac{π}{3}

(b) \frac{π}{6}

(c) cos^{-1}\frac{\sqrt{2}}{3}

(d) cos^{-1}\frac{2}{\sqrt{3}}

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Correct choice is (b) \frac{π}{6}

To explain: Given that, |\vec{a}|=2 \,and \,|\vec{b}|=\sqrt{3}

Also, \vec{a.} \,\vec{b}=4

The angle between two vectors is given by

cosθ=\frac{|\vec{a}|.|\vec{b}|}{\vec{a}.\vec{b}}

∴cosθ=\frac{2.\sqrt{3}}{4}=\frac{\sqrt{3}}{2}

∴θ=cos^{-1}\frac{\sqrt{3}}{2}=\frac{π}{6}.