The only lines that are in the same plane that do not intersect are:
1. Lines of finite length (eg 1 6" line on the floor at one end of the room and another 8" line at the other end)
2. Parallel lines
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parallel lines If they are not on the same plane and never intersect they are skew
Lines which are parallel. All other lines on the same plane eventually intersect.
No, if the lines were in the same plane they would be parallel and never intersect
If they are not parallel and do not intersect then they would not be in the same plane (not possible), but they would be called skew lines.
If the 2 lines lie in the same plane, and they are not parallel, then they will intersect at some point. If the 2 lines are skew lines, then they are not in the same plane, and they will not intersect (but they are Not Parallel)