Question

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

Explanation:

Step1: Recall line relationship definitions

• Non - coplanar: Lines not in same plane. But line \(a\) (vertical in plane \(M\)) and line \(d\) (horizontal, intersecting plane \(M\))—wait, actually, from diagram, \(a\) is vertical (in a plane) and \(d\) is horizontal, but let's check other options.
• Parallel: Lines that never meet, same direction, coplanar.
• Perpendicular: Form \(90^\circ\) angle.
• Skew: Non - coplanar, non - parallel, non - intersecting.

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

• Line \(a\) is vertical (in a plane, say \(M\)) with a right angle mark to \(d\)? Wait, the diagram has a right angle between \(a\) and \(d\)? Wait, no—wait, the right angle is between \(a\) and the horizontal line? Wait, no, looking at the diagram: line \(a\) is vertical (up - down), line \(d\) is horizontal (left - right), and there's a right angle symbol between them. Wait, no, maybe I misread. Wait, the options: let's re - evaluate.

Wait, no—wait, the correct approach:

• Non - coplanar: No, because \(a\) and \(d\) intersect? Wait, no, in the diagram, \(a\) is in plane \(M\), \(d\) is a horizontal line (maybe in plane \(N\) or intersecting \(M\)). Wait, no, the right angle symbol: if two lines form a right angle, they are perpendicular. Wait, but let's check the options again. Wait, the diagram: line \(a\) is vertical, line \(d\) is horizontal, and there's a right angle (the little square) between them. So they are perpendicular? Wait, no—wait, maybe I made a mistake. Wait, the options: parallel (same direction, never meet), perpendicular (90 degrees), skew (non - coplanar, non - parallel, non - intersecting).

Wait, no—wait, line \(a\) and \(d\): do they intersect? The diagram shows a right angle between them, so they are perpendicular. Wait, but let's check the definitions again.

Wait, no—wait, the correct answer: if two lines form a right angle (90 degrees), they are perpendicular. So the answer is perpendicular? Wait, no—wait, maybe I messed up. Wait, the diagram: line \(a\) is vertical, line \(d\) is horizontal, and there's a right angle symbol, so they are perpendicular. So the correct option is "perpendicular".

Wait, no—wait, let's re - check. The options are non - coplanar, parallel, perpendicular, skew.

• Non - coplanar: No, because they intersect (or are in a plane where they form a right angle, so coplanar).
• Parallel: No, because parallel lines don't meet and have same direction. \(a\) is vertical, \(d\) is horizontal—different directions.
• Perpendicular: Yes, because they form a right angle (the right angle symbol in the diagram).
• Skew: No, because skew lines are non - coplanar, non - parallel, non - intersecting. These lines intersect (or are coplanar and form a right angle), so not skew.

So the correct option is "perpendicular".

Answer:

perpendicular (the option with "perpendicular" text)