Difference between Perpendicular, Orthogonal and Normal It seems to me that perpendicular, orthogonal and normal are all equivalent in two and three dimensions.  I'm curious as to which situations you would want to use one term over the other in two and three dimensions. 

Also... what about higher dimensions?  It seems like perpendicular and normal would not have a nice meaning whereas orthogonal would as it is defined in terms of the dot product. 

Can someone give me a detailed breakdown as to the differences in their meanings, their uses and the situations for which each should be used?
In two or three dimensions, I agree, perpendicular is more natural than orthogonal.

In higher dimensions, or if the dimension is represented by an unknown, both are correct, but I think orthogonal is preferable.

Here's an excerpt from Wikipedia (https://en.wikipedia.org/wiki/Orthogonality):


  In mathematics, orthogonality is the generalization of the notion of perpendicularity to the linear algebra of bilinear forms.


Normal can be used in any dimension, but it usually means perpendicular to a curve or surface (of some dimension).
Perpendicular lines may or may not touch each other. Orthogonal lines are perpendicular and touch each other at junction.