Physics with Calculus/Mechanics/Relative Motion

In an approximation termed Galilean relativity, when two objects are moving at $\vec{u}$ and $\vec{v}$ relative to a common inertial reference frame, the relative velocity between the two objects, in the frame of reference where one of them is still, is

$\vec{v}_{\mathrm{ref}} = \vec{v} - \vec{u}$