The position vector of a particle is a vector drawn from the origin of the reference frame to the particle. It expresses both the distance of the point from the origin and its direction from the origin. In three dimensions, the position vector r can be expressed as r = ( x , y , z ) = x x ^ ^ + y y ^ ^ + z z ^ ^ , where x , y , and z are the Cartesian coordinates and x ^ ^ , y ^ ^ and z ^ ^ are the unit vectors along the x , y , and z coordinate axes, respectively. The magnitude of the position vector | r | gives the distance between the point r and the origin. | r | = x 2 + y 2 + z 2 . The direction cosines of the position vector provide a quantitative measure of direction. In general, an object's position vector will depend on the frame of reference; different frames will lead to different values for the position vector.