Question

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

Explanation:

Step1: Recall definitions

• Non - coplanar: Lines that do not lie on the same plane. But skew lines are non - coplanar and non - intersecting.
• Parallel: Lines in the same plane that do not intersect.
• Perpendicular: Lines that intersect at a right angle (\(90^{\circ}\)).
• Skew: Non - coplanar, non - intersecting lines.

Step2: Analyze the relationship between lines \(a\) and \(d\)

• Line \(a\) lies on plane \(N\) and line \(d\) lies on plane \(M\).
• Lines \(a\) and \(d\) are not parallel (they are not in the same plane and do not have the same direction), not perpendicular (no right - angle intersection as they are not in the same plane to form a right angle), and not non - coplanar (skew is a more specific term for non - coplanar non - intersecting lines).
• Lines \(a\) and \(d\) are non - coplanar and non - intersecting.

Answer:

skew.