Cosine Formula for Dot Product

Theorem
Let $\mathbf v,\mathbf w$ be two non-zero vectors in $\R^n$.

The dot product of $\mathbf v$ and $\mathbf w$ can be calculated by:


 * $\mathbf v \cdot \mathbf w = \norm {\mathbf v} \norm {\mathbf w} \cos \theta$

where:


 * $\norm {\, \cdot \,}$ denotes vector length and


 * $\theta$ is the angle between $\mathbf v$ and $\mathbf w$.

Also see

 * Angle Between Vectors in Terms of Dot Product