The angle between two vectors is obtained from their dot product: = ^ -1 ( a b ab )

PHYSICS · Subjective · CBSE · Physics · System of Particles and Rotational Motion · System of Particles and Rotational Motion

Problem

The angle between two vectors is obtained from their dot product:

\theta=\cos^{-1}\left(\frac{\mathbf{a}\cdot\mathbf{b}}{ab}\right).

Explain why it is not always obtained from

\theta=\sin^{-1}\left(\frac{|\mathbf{a}\times\mathbf{b}|}{ab}\right).