A position vector describes the position of a point relative to a fixed origin. For example, the position vector of a point P describes the location of P relative to an origin O:

A displacement vector describes how to move from one point to another. For instance, the displacement vector from point A to point B is given by subtracting position vectors:

Thus, position vectors identify points relative to an origin, while displacement vectors represent movement or translation between points.

Example

If OB=i−2j+3k and OA=2i+j+k, find AB.