You should already be familiar with the equation of a straight line in a 2D plane as being . This section takes that work a step further. It allows us to express the equation of a straight line in 3D space in a similar format.
Take a straight line through the point A with direction vector . R is another point on that line. The position vector (from an arbitrary origin) of A is , and of R is . The vector is a multiple, , of .
It follows that the position of a point R on the line is given by:
2 July 2013, Created with GeoGebra