Question

are any pair of perpendicular lines coplanar?

Answer 1

here is our plane (imagine a piece of paper or something)and here is a line in that plane...

Answer 2

now is there any way to make a line perpendicular to this one that is not in the same page?

Answer 3

this perpendicular would be in the page as well, so that would suggest that the perpendiculars are co-planar.

consider one thing though: what if I stabbed my pencil right though the paper, into the desk? if that pencil represents a line in space, can I make it so that my pencil is perpendicular to the line drawn on the paper?

If you cannot visualize it, grab a piece of paper, draw the line, and try to hold your pencil perpendicular to the line while \(not\) lying on the paper. If you can do it, the answer is "false". If you cannot, then the answer is "true".