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 perpendicular. lines a and b must be skew lines a and b must be parallel. lines a and b cannot be parallel.

Explanation:

If two lines lie on the same plane (the third - plane in this case), they cannot be skew (since skew lines do not lie on the same plane). Parallel planes \(Q\) and \(R\) have lines \(a\) (in \(Q\)) and \(b\) (in \(R\)). If there is a plane that contains both \(a\) and \(b\), by the definition of parallel lines (two lines in the same plane that do not intersect), and since the original planes \(Q\) and \(R\) are parallel (so \(a\) and \(b\) do not intersect), the only possibility for two non - intersecting lines in the same plane is that they are parallel. Perpendicular lines intersect (at a right angle), and we know \(a\) and \(b\) do not intersect (because they are in parallel planes \(Q\) and \(R\) initially, and if they were in a new plane together, they still don't intersect as the original planes are parallel).

Answer:

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