## Moving Particles, Position Vectors and Relative Position Vectors

For any particle moving on a flat surface, we can find the position vector relative to a fixed point, by counting to the right x units, up y units and writing downIf instead we move to the left or down thenorare negative. Suppose though that the particle starts from the pointwith velocityAfterseconds it will have moved by a vectorand it' s new position will be atThis is illustrated on the graph below.

If we have two particles, A and B, both moving Then the position vector of B relative to A is given by

Ifthen the position vector of B relative to A is given by

and the velocity of B relative to A is. If the velocities of both particles are constant, as in this case then the relative velocity is constant.

If particle A is initially atmoving with velocityand B is atat the same time, moving with velocity 9i+10j the the position vector of A at any time is

The position vector of B relative to A is and the velocity of B relative to A is