Intersection of Two Planes in R3: Always a Line?

[mirandasatterley]

Homework Statement

True or False: The intersection of two planes in R3 is always a line.

The Attempt at a Solution

I'm pretty sure that this statement is true because two planes can only be parallel, or they must intersect in a line because the are infinate.

But I have no ideas on how to prove this mathematically. Any ideas?

 

[Mathdope]

Are you familiar with the cross product? If so, consider the cross product of the normals to each plane.

By the way, what if the planes are parallel?