Pythagorean theorem

We are, very obviously, familiar with the Pythagorean theorem.

$$a^2+b^2=c^2$$

We can extend to vectors, specifically orthogonal vectors, where $\vec{x},\vec{y}\in {\mathbb{R}}^n$, as followed.

$$\Vert \vec{x}+\vec{y}{\Vert }^2=\Vert \vec{x}{\Vert }^2+\Vert \vec{y}{\Vert }^2$$