Angle Between Vectors in Terms of Dot Product

Theorem
The angle between two non-zero vectors in $\R^n$ can be calculated by:

where:


 * $\mathbf v \cdot \mathbf w$ represents the dot product of $\mathbf v$ and $\mathbf w$


 * $\mathbf \Vert \cdot \Vert$ represents vector length.


 * $\arccos$ represents arccosine

Also see

 * Angle Between Non-Zero Vectors Always Defined