> $\vec v_P \cdot (\vec r_P - \vec r_Q)= \vec v_Q \cdot (\vec r_P - \vec r_Q)$

@mechanist That isn't true if the body is rotating because the two velocities are not necessarily equal.

@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 $\vec r_2 - \vec r_1$.

@JohnRennie ps - can also be written as $(\vec v_P -\vec v_Q) \cdot (\vec r_P - \vec r_Q)= 0$