# Parallelogram Law

## Theorem

Let $\mathbf a$ and $\mathbf b$ be vectors.

Consider a parallelogram, two of whose adjacent sides represent $\mathbf a$ and $\mathbf b$ (in magnitude and direction).

Then the diagonal of the parallelogram through that common point represents the magnitude and direction of $\mathbf a + \mathbf b$, the sum of $\mathbf a$ and $\mathbf b$.