Physics with Calculus/Mechanics/Relative Motion

In an approximation termed Galilean relativity, when two objects are moving at $\overrightarrow{u}$ and $\overrightarrow{v}$ 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

${\overrightarrow{v}}_{\mathrm{r}\mathrm{e}\mathrm{f}}=\overrightarrow{v}-\overrightarrow{u}$