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True or false: A plane and a line either intersect or are parallel.

I know that this is true but I want to make sure my reasoning is sound. So I think it is true because by definition of a plane and a line in the third dimension. Is this correct or is there a better way to explain this?

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Take two distinct points on the line. Either they are the same distance from the plane (and on the same side of the plane)--in which case the line is parallel to the plane, or they are of different distance from the plane--in which case the line must intersect the plane).

Flesh out that insight and you'll be done.

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  • $\begingroup$ Thank you so much!! $\endgroup$ Sep 17 '18 at 0:21

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