Question

planes q and r are parallel planes. plane q contains line a. plane r contains line b. if a third plane could be drawn which contains both lines a and b, then lines a and b must be parallel. lines a and b cannot be parallel. lines a and b must be skew. lines a and b must be perpendicular.

Explanation:

• If two lines \(a\) and \(b\) lie in two parallel planes \(Q\) and \(R\) respectively, and there exists a third plane that contains both \(a\) and \(b\), then by the definition of parallel lines (two lines are parallel if they lie in the same plane and do not intersect), lines \(a\) and \(b\) must be parallel.
• Skew lines do not lie in the same plane, so if a plane contains both \(a\) and \(b\), they cannot be skew.
• There is no information given that would make them perpendicular. And the fact that a plane can contain both contradicts the "cannot be parallel" option.

Answer:

lines a and b must be parallel.