Distance between two orthonormal vectors

Two vectors $x,y\in\mathbb{R}^n$ each have length $1$ and are perpendicular to each other. The length $\|x-y\|$ equals $\sqrt a$ for an integer $a$. What is $a$?

$a=2$. Expanding, $\|x-y\|^2=\|x\|^2-2\,x\cdot y+\|y\|^2=1-0+1=2$; this is just Pythagoras for the right isosceles triangle with unit legs.