Parallelogram Equation for Vectors

Theorem

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

Then

$$||\mathbf{u}+\mathbf{v}|{|}^2+||\mathbf{u}-\mathbf{v}|{|}^2=2(||\mathbf{u}|{|}^2+||\mathbf{v}|{|}^2)$$