# Parallelogram Law for Vector Subtraction

## Theorem

Let $\mathbf u$ and $\mathbf v$ be vectors.

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

Then the diagonal of the parallelogram connecting the terminal points of $\mathbf u$ and $\mathbf v$ represents the magnitude and direction of $\mathbf u - \mathbf v$, the difference of $\mathbf u$ and $\mathbf v$.

## Proof

We can construct a parallelogram as follows:

and the construction is apparent.