Essential University Physics: Volume 1 (4th Edition) Clone

It is given that $\vec{A}^{\,}.\vec{B}^{\,}=\frac{1}{2}|\vec{A}^{\,}\times \vec{B}^{\,}|$ We know that $\vec{A}^{\,}.\vec{B}^{\,}=ABcos\theta$ $\vec{A}^{\,}\times \vec{B}^{\,}=ABsin\theta$ $\implies ABcos\theta=\frac{1}{2} ABsin\theta$ $2=tan\theta$ $\theta=tan^{-1}(2)=63.4^{\circ}$