Question

which are lines that will intersect? a and b which are perpendicular lines? which are skew lines? a and b a and c b and d

Explanation:

Step1: Recall definitions

• Intersecting lines: Lines that cross each other at a point.
• Perpendicular lines: Lines that intersect at a right - angle ($90^{\circ}$).
• Skew lines: Non - parallel, non - intersecting lines in 3 - D space.

Step2: Analyze each pair

• For \(a\) and \(b\): They are in the same plane (plane \(M\)) and intersect.
• For \(a\) and \(c\): They are in different planes, non - parallel and non - intersecting (skew).
• For \(b\) and \(d\): \(b\) is in plane \(M\), \(d\) is in the base plane. They are non - parallel and non - intersecting (skew).

Answer:

• Which are perpendicular lines? \(b\) and \(d\) (assuming from the right - angle symbol in the base plane for line \(d\) and the vertical line \(b\) in plane \(M\) which is perpendicular to the base plane).
• Which are skew lines? \(a\) and \(c\), \(b\) and \(d\)