Question

What is the difference between intersecting and perpendicular lines? Can two lines exist that are not intersecting or parallel? Explain your answer.

Answer 1

Intersecting lines are any two lines that cross paths.
Perpendicular lines also intersect, but must be at a 90 degree angle to each other.
Yes, you can have two lines that are not intersecting.. they're called parallel lines, and they remain the same distance apart forever.

Answer 2

perpendicular lines intersect at right angles
second part - no not in two dimensions but they can in three dimensional space (these are called skew lines)