Problem

Angle between two vectors is obtained by their dot product (not from cross product) i.e.

\theta = \cos^{-1} \left( \frac{\mathbf{A} \cdot \mathbf{B}}{AB} \right)

\text{It is not always, } \sin^{-1} \left\{ \frac{|\mathbf{A} \times \mathbf{B}|}{AB} \right\}

Explain the reason why

\theta

is not always given by the following relation:

\theta = \sin^{-1} \left\{ \frac{|\mathbf{A} \times \mathbf{B}|}{AB} \right\}