Relationship between Dot Product and Norm in Rn

Theorem

Let $\mathbf{u},\mathbf{v}$ vectors in $R^n$

Then

$$\mathbf{u}\cdot \mathbf{v}=\frac{1}{4}||\mathbf{u}+\mathbf{v}|{|}^2-\frac{1}{4||\mathbf{u}-\mathbf{v}}|{|}^2$$