Given points A and B in R^{3} (3D) with position vectors ** a** and

Suppose we are in a starship located at point A (relative to some fixed galactic cartesian coordinates) and we are required to set course for the space station located at point B. To do this we need to tell the ship the position vector it should have at any given time, t. We set t=0 when we have position vector

Let

for 0 O t O 1

You can easily check that,

and, for instance, we reach the point halway between A and B when t = 1/2, so the halfway point is,

By letting t be any real number we can get to any point along the line through A and B.