If Planes Q and R are parallel planes. Plane Q contains line a. Plane R contains line b. a third plane could be drawn which contains both lines a and b, then

Since parallel lines need to be in the same plane, if there were a plane (the third one) that had both lines, this would meet the requirements for parallel lines. So its parallel.

If a third plane could be drawn which contains both lines a and b, then lines a and b must be parallel. if two lines do not intersect on the same plane, they are parallel. Furthermore, if a line is in a plane and another line is in a parallel plane, you cannot draw another plane which contains both lines a and b, only if the lines are parallel.