Explain why a line can never intersect a plane in exactly two points. Why can a line never intersect a plane in exactly two points?
I know this seems like a really simple question, but I'm having a hard time figuring out how to answer it. I also tried googling the question but I couldn't find an answer for exactly what I'm looking for.

A plane is a convex set. A convex (i.e. linear) combination of any two points in a convex set will be inside the set. So if you have two distinct points in the plane, you automatically have infinite points inside the plane. 
