angle between vectors

The angle between vectors can be determined with dot product:

$$\cos \theta =\frac{\vec{u}\cdot \vec{v}}{|\vec{u}|\cdot |\vec{v}|}$$

or alternatively using cross product:

$$\sin \theta =\frac{\vec{u}\times \vec{v}}{|\vec{u}|\cdot |\vec{v}|}$$