# How do I find the angle between two vectors using the law of cosines?

Oct 25, 2014

Law of Cosines for Vectors

$\vec{v} \cdot \vec{w} = | \vec{v} | | \vec{w} | \cos \theta$

By solving for $\theta$,

$R i g h t a r r o w \cos \theta = \frac{\vec{v} \cdot \vec{w}}{| \vec{v} | | \vec{w} |} R i g h t a r r o w \theta = {\cos}^{- 1} \left(\frac{\vec{v} \cdot \vec{w}}{| \vec{v} | | \vec{w} |}\right)$

I hope that this was helpful.