@JohnRennie, idk I think the equation works for a rotating body too... Assume rotation about a stationary axis at $\omega$, then velocities of points $\vec r_1$ and $\vec r_2$ are $\vec \omega \times \vec r_1$ and $\vec \omega \times \vec r_2$, so their relative velocity is $\vec \omega \times (\vec r_2 - \vec r_1)$ which must be perpendicular to $\vec r_2 - \vec r_1$.