If $\vec{a} $ and $\vec{b}$ are unit vectors, then the angle between $\vec{a}$ and $\vec{b}$ for $\vec{a}+\sqrt{3}\vec{b}$ to be a unit vector is given by :

$\frac{\pi }{6}$ $\frac{5\pi }{6}$ $\frac{\pi }{3}$ $\frac{2\pi }{3}$

$\frac{5\pi }{6}$