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In Euclidean geometry, if they are coplanar they must intersect. But if they are in different planes, they may not. The following example will illustrate this:

Picture yourself in a cuboid room - ie a normal shaped room. Stand with your back to one of the walls. Ray 1 forms the join of the wall behind you and the floor. Ray 2 is the line where the wall facing you meets one of the side walls. Rays 1 and 2 are not parallel but they can never meet - because they are not in the same plane.

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Q: Do rays that are not parallel intersect?
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