If the velocities of particles $A$ and $B$ with respect to the ground are ${\overrightarrow v _A}$ and ${\overrightarrow v _B}$ respectively,then:
$(a)$ Write the formula for the velocity of $A$ with respect to $B$.
$(b)$ Write the formula for the velocity of $B$ with respect to $A$.
$(c)$ Is the relation ${\overrightarrow v _{AB}} = -{\overrightarrow v _{BA}}$ correct?

(C) The velocity of particle $A$ with respect to particle $B$ is given by: ${\overrightarrow v _{AB}} = {\overrightarrow v _A} - {\overrightarrow v _B}$.
$(b)$ The velocity of particle $B$ with respect to particle $A$ is given by: ${\overrightarrow v _{BA}} = {\overrightarrow v _B} - {\overrightarrow v _A}$.
$(c)$ Yes,the relation is correct. Since ${\overrightarrow v _{AB}} = {\overrightarrow v _A} - {\overrightarrow v _B}$ and ${\overrightarrow v _{BA}} = {\overrightarrow v _B} - {\overrightarrow v _A}$,we can see that ${\overrightarrow v _{AB}} = - ( {\overrightarrow v _B} - {\overrightarrow v _A} ) = - {\overrightarrow v _{BA}}$.