Question

identifying types of lines in three dimensions
which are lines that will intersect?
which are perpendicular lines?
which are skew lines?

Explanation:

• Intersecting lines: Lines \(a\) and \(b\) lie in the same plane \(M\) and cross each other.
• Perpendicular lines: Lines \(a\) and \(b\) form a right - angle (as indicated by the small square in the diagram), so they are perpendicular.
• Skew lines: Skew lines are non - parallel and non - intersecting lines that do not lie in the same plane. Lines \(b\) and \(c\) are in different planes (\(b\) is in plane \(M\) and \(c\) is in a different non - parallel plane), and they neither intersect nor are parallel.

Answer:

• Which are lines that will intersect? \(a\) and \(b\)
• Which are perpendicular lines? \(a\) and \(b\)
• Which are skew lines? \(b\) and \(c\)