Parallelogram Law

Theorem
Let $\vec a$ and $\vec b$ be vectors.

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


 * ParallelogramLaw.png

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