Intersection of Two Planes in R3: Always a Line?

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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?
 
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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?
 
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