3.7.4—Straight lines

A line through point a in direction d is r=a+λd. Different parameter values move along the same line, and a non-zero scalar multiple of d gives the same direction.

Use the position vector and direction vector separately; compare lines by solving component equations for a common point and compatible parameters.

r=(1,2)+λ(3,−1) passes through (1,2) and has direction (3,−1).

A point on a line is not itself a direction vector, and changing the parameter origin changes a but not the geometric line.