Vector $\mathbf{v}$ and $\mathbf{v'}$ make angles $\alpha , \beta, \gamma$ and $\alpha ', \beta', \gamma$' with the coordinate axes respectively.
$\phi$ is the angle between $\mathbf{v}$ and $\mathbf{v'}$.
Why is $\cos(\phi)=\cos(\alpha)\cos(\alpha')+\cos(\beta)\cos(\beta')+\cos(\gamma)\cos(\gamma')$?