Page 242 - Elementary_Linear_Algebra_with_Applications_Anton__9_edition

are called parametric equations for l.

Figure 3.5.4

is parallel to v.

EXAMPLE 4 Parametric Equations of a Line

The line through the point and parallel to the vector has parametric equations

EXAMPLE 5 Intersection of a Line and the -Plane

(a) Find parametric equations for the line l passing through the points and .
(b) Where does the line intersect the -plane?

Solution (a) is parallel to l and lies on l, the line l is given by

Since the vector

Solution (b) , that is, where . Substituting this value of t in the

The line intersects the -plane at the point where
parametric equations for l yields, as the point of intersection,