No. Skew lines are never coplanar.
Stand in a cuboid room and consider the line where the opposite wall and the floor meet.
Consider also the line where the walls behind you and to your right meet.
Those two lines are not coplanar.
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Yes.
are two lines that are not parallel, coplanar, and do not intersect
Two lines that are perpendicular to the same plane are coplanar. This means that they lay on the same plane.
parallel lines
Parallel lines remain equal distance apart and never intersect with each other.