Suppose that a point O is chosen as the origin (in the plane, or in 3-dimensional space). Given any point P, the position vector p of the point P is the vector represented by the directed line segment $OP$→.

In mechanics, the position vector of a particle is often denoted by r, which is a function of the time t, giving the position of the particle as it moves. If Cartesian coordinates are used, then r = xi+yj+zk, where x, y, and z are functions of t.