Question

consider the diagram. lines a and d are
○ non - coplanar.
○ parallel.
○ perpendicular.
○ skew.

Explanation:

1. Recall the definitions:

• Non - coplanar lines do not lie on the same plane. But from the diagram, line \(a\) is in plane \(M\) (and also intersects plane \(N\)) and line \(d\) is also in a plane that intersects with plane \(M\), and they share a common point, so they are coplanar. So the "non - coplanar" option is wrong.
• Parallel lines are coplanar and never intersect. But line \(a\) and line \(d\) intersect (they share a common point), so they are not parallel. So the "parallel" option is wrong.
• Perpendicular lines are coplanar, intersect at a right angle (\(90^{\circ}\)). From the diagram, there is a right - angle symbol between line \(a\) and line \(d\), which means they intersect at \(90^{\circ}\).
• Skew lines are non - coplanar and non - intersecting. Since line \(a\) and line \(d\) intersect, they are not skew. So the "skew" option is wrong.

Answer:

perpendicular (the option with the text "perpendicular")