Intersection of 2 planes

mirandasatterley

1. The problem statement, all variables and given/known data

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

3. 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?