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:

Step1: Recall the property of lines in parallel planes

If two lines lie in parallel planes and a third plane contains both lines, then the two lines are coplanar.

Step2: Analyze the relationship of coplanar lines in parallel planes

Since planes \(Q\) and \(R\) are parallel, and a third plane contains lines \(a\) (in plane \(Q\)) and \(b\) (in plane \(R\)). Skew lines are non - coplanar. If two lines are coplanar (because a single plane contains both), and the original planes (\(Q\) and \(R\)) are parallel, the only way for two lines (one in each parallel plane) to be coplanar is that they are parallel. Perpendicular lines would require a specific angle condition which is not guaranteed here. If they were not parallel (and coplanar), they would intersect, but two lines in parallel planes cannot intersect.

Answer:

lines a and b must be parallel