Find the expression for the relative velocity of any two particles moving in a frame of reference.

(N/A) Consider two particles $A$ and $B$ in a frame of reference with velocities $\vec{V}_{A}$ and $\vec{V}_{B}$ respectively.
The velocity of particle $A$ with respect to particle $B$ is given by the vector difference:
$\vec{V}_{AB} = \vec{V}_{A} - \vec{V}_{B}$
Similarly,the velocity of particle $B$ with respect to particle $A$ is given by:
$\vec{V}_{BA} = \vec{V}_{B} - \vec{V}_{A}$
From these expressions,we can observe that:
$\vec{V}_{AB} = -\vec{V}_{BA}$ and $|\vec{V}_{AB}| = |\vec{V}_{BA}|$.
In a general frame of reference $X$,if particles $P$ and $Q$ have velocities $\vec{V}_{PX}$ and $\vec{V}_{QX}$ relative to frame $X$,then the relative velocity of $P$ with respect to $Q$ is:
$\vec{V}_{PQ} = \vec{V}_{PX} - \vec{V}_{QX}$.