Question

are the lines in the diagram perpendicular, parallel, skew, or none of these? l and m: l and n: m and n:

Explanation:

Step1: Recall line - relationship definitions

Parallel lines are in the same plane and never intersect. Perpendicular lines intersect at a right - angle. Skew lines are non - coplanar and do not intersect.

Step2: Analyze \(m\) and \(n\)

Lines \(m\) and \(n\) are in different planes and do not intersect. They are skew.

Step3: Analyze \(l\) and \(n\)

Lines \(l\) and \(n\) are in the same plane and are parallel (they do not intersect and have the same direction in the plane).

Step4: Analyze \(l\) and \(m\)

Lines \(l\) and \(m\) are in different planes and do not intersect. They are skew.

Answer:

\(m\) and \(n\): skew
\(l\) and \(n\): parallel
\(l\) and \(m\): skew