Question

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

Explanation:

Step1: Analyze \( l \) and \( m \)

Lines \( l \) and \( m \) are in the same plane \( \mathcal{A} \), and they do not intersect and are not parallel.

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

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

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

Lines \( m \) and \( n \) intersect at a right - angle (as indicated by the right - angle symbol in the diagram).

Answer:

\( l \) and \( m \): skew; \( l \) and \( n \): skew; \( m \) and \( n \): perpendicular