Given two lines $a$ and $d$ that are non-coplanar, which of the following best describes their relationship?

• A. They are skew.
• B. They are parallel.
• C. They are perpendicular.
• D.

Answer: (A)

Verified step by step guidance

1. Understand the definitions of the relationships between two lines in three-dimensional space: Parallel lines lie in the same plane and never intersect; perpendicular lines intersect at a right angle; skew lines are lines that are not in the same plane and do not intersect.
2. Identify that the problem states the two lines \( a \) and \( d \) are non-coplanar, meaning they do not lie in the same plane.
3. Recall that if two lines are non-coplanar, they cannot be parallel because parallel lines must lie in the same plane.
4. Also, since they are non-coplanar, they cannot intersect, so they cannot be perpendicular (which requires intersection at a right angle).
5. Conclude that the only relationship that fits non-coplanar lines is that they are skew lines.