Consider two observers observing a single moving object,and one observer observing two moving objects. Explain the concept of relative velocity in these scenarios.

(N/A) Consider two inertial frames of reference $A$ and $B$ moving with constant velocity relative to each other.
Suppose one observer in frame $A$ and another observer in frame $B$ study the motion of a particle $P$.
Let the position vectors of the moving particle $P$ at time $t$ with respect to the origins of frames $A$ and $B$ be $\overrightarrow{r_{P,A}} = \overrightarrow{OP}$ and $\overrightarrow{r_{P,B}} = \overrightarrow{O'P}$ respectively,and the position vector of $O'$ with respect to $O$ be $\overrightarrow{r_{B,A}} = \overrightarrow{OO'}$.
From the geometry of the vectors,$\overrightarrow{OP} = \overrightarrow{OO'} + \overrightarrow{O'P}$.
Therefore,$\overrightarrow{r_{P,A}} = \overrightarrow{r_{B,A}} + \overrightarrow{r_{P,B}}$.
Differentiating with respect to time $t$:
$\frac{d}{dt}(\overrightarrow{r_{P,A}}) = \frac{d}{dt}(\overrightarrow{r_{P,B}}) + \frac{d}{dt}(\overrightarrow{r_{B,A}})$.
Thus,$\overrightarrow{v_{P,A}} = \overrightarrow{v_{P,B}} + \overrightarrow{v_{B,A}}$.
Here,$\overrightarrow{v_{P,A}}$ is the velocity of particle $P$ relative to frame $A$,$\overrightarrow{v_{P,B}}$ is the velocity of particle $P$ relative to frame $B$,and $\overrightarrow{v_{B,A}}$ is the velocity of frame $B$ relative to frame $A$.