I thought skew lines never intersect. It's the definition, two lines that are not parallel but are not in the same plane, such that they never intersect. also parallel lines never intersect, unless they are the same line (in which case they intersect everywhere, but this is a fairly trivial case, no?)
IDK...if two planes never intersect, their intersection is never a plane, unless they are the same plane (think of two pieces of paper on top of each other)