# Parallelogram Identity The **parallelogram identity** says that for [[vectors]] $\vec{u}$ and $\vec{v}$ then the length $\|\cdot\|$ satisfies: $$ \|\vec{u} + \vec{v}\| + \|\vec{u} - \vec{v}\| = 2 \|\vec{u}\| + 2\|\vec{v}\| $$