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.
• Parallel: Lines in the same plane that never intersect.
• Perpendicular: Lines that intersect at a right angle (90 degrees).
• Skew: Non - parallel, non - intersecting lines that are not coplanar.

Step2: Analyze lines \(a\) and \(d\)

• Lines \(a\) and \(d\) are not parallel (their directions are different).
• They do not intersect (as per the diagram).
• They are not coplanar (line \(a\) is on plane \(N\) and line \(d\) is on a different plane - we can consider the orientation in 3D space).

Since lines \(a\) and \(d\) are non - parallel, non - intersecting, and non - coplanar, they are skew.

Answer:

skew