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:

• Parallel planes: Planes \(Q\) and \(R\) are parallel. If a third plane contains lines \(a\) (in plane \(Q\)) and \(b\) (in plane \(R\)), then by the property of parallel planes and lines within planes, if two lines lie in parallel planes and another plane contains both of them, the two lines must be parallel.
• Skew lines: Skew lines are non - parallel and non - intersecting lines that do not lie in the same plane. But since there is a plane that contains both \(a\) and \(b\), they are not skew.
• Perpendicular lines: There is no information given about the angle between \(a\) and \(b\) to suggest they are perpendicular. Just because a plane contains them does not imply a right - angle relationship.
• Non - parallel lines: If lines were non - parallel (intersecting or skew), but since they lie in parallel planes \(Q\) and \(R\) (initially) and a single plane contains them, they cannot be non - parallel (because intersecting lines would require the two original planes \(Q\) and \(R\) to intersect which they don't as they are parallel, and we already ruled out skew).

Answer:

lines \(a\) and \(b\) must be parallel.