Position vectors and displacement vectors

We are now free to deal with displacement and position vectors from an analytical viewpoint. The position vector to the general coordinate point (x,y,z) is usually written as . This is a vector (called which points from the origin to the point (x,y,z) and has a magnitude of .)

A displacement vector from the point to the point has components or can be written as . This is a vector the ``starts at'' the first point (the one with the ``1'' subscripts) and points toward the second point. Notice that the magnitude of this vector is simply the actual Euclidian distance (the square root of the sum of the squares of the differences in the coordinates) between the two points.