The University of Sydney - School of Mathematics and Statistics

The parametric scalar equations	Page 2 of 3

Suppose that the point P₀ has coordinates x₀,y₀,z₀, and the non-zero vector v has components a,b,c.

Let x,y,z be the coordinates of an arbitrary point P on the line l.

Then

and the position vectors of P₀ and P are given by

and

respectively. The parametric vector equation may be rewritten as

that is,

with t R. These equations are called parametric scalar equations of the line.