Let r_P and r_Q be the position vectors of particles P and Q with respect to some frame of reference with origin O, as shown in the diagram. The position vector of P relative to Q is r_P−r_Q. If $v_P={\dot{r}}_P$ and $v_Q={\dot{r}}_Q$, then v_P and v_Q are the velocities of P and Q relative to the frame of reference with origin O and v_P−v_Q is the velocity of P relative to Q. If $a_P={\dot{v}}_P$ and $a_Q={\dot{v}}_Q$, then a_P and a_Q are the accelerations of P and Q relative to the frame of reference with origin O, and a_P−a_Q is the acceleration of P relative to Q. These quantities may be called the relative position, the relative velocity, and the relative acceleration of P with respect to Q.

Position of P relative to Q

These notions are important when there are two or more frames of reference, each with an associated observer.