$\cos^2 \alpha + \cos^2 \beta + \cos^2 \gamma =1$ 
Let be $\alpha, \beta, \gamma$  the angles between a generic direction in 3D and the axes $x,y,z$, respectively.
Prove that
$\cos^2 \alpha + \cos^2 \beta + \cos^2 \gamma =1$.

PS: the 2D case is trivial. But I can't prove the 3D case.

Hint: If $u$ and $v$ are vectors making an angle $\theta$ then $$u\cdot v=||u||\,||v||\cos(\theta).$$
