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:

• Definition of parallel lines: Two lines are parallel if they lie in the same plane and do not intersect.
• Given conditions: Planes \(Q\) and \(R\) are parallel. Line \(a\) is in plane \(Q\), line \(b\) is in plane \(R\). A third plane contains both \(a\) and \(b\).
• Analysis of options:
• If two lines \(a\) and \(b\) lie in the same plane (the third - drawn plane), they cannot be skew (skew lines do not lie in the same plane).
• Just because they are in a plane together does not mean they must be perpendicular. There is no information about the angle between them to suggest perpendicularity.
• If two non - intersecting lines lie in the same plane, they are parallel. Since planes \(Q\) and \(R\) are parallel, lines \(a\) and \(b\) do not intersect (because if they intersected, planes \(Q\) and \(R\) would intersect at that point, which contradicts the fact that \(Q\) and \(R\) are parallel). And now they lie in the same (third) plane.

Answer:

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