Do rays that are not parallel intersect?

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.