At a certain instant, particles and have position vectors and velocities given by: Matlab/Mathematica input:
rP = [2,-5]
rQ = [-3,-6]
vP = [-7,-8]
vQ = [-2,-8]
What is the rate of change of the distance between points and ?

Explanation:

The vectors are:

            Particle P

            Particle Q

            Particle P

            Particle Q

The rate of change of the relative positions of point P and Q is the relative velocity of one respect to the other.

The relative velocity of Q respect to P, in meter per second, is:

And the rate of change of the distance between points P and Q is the magnitude of the vector, which is 7m/s.