There is no general definition of "parallel" that is agreed upon. But a good one would be that everywhere the minimum distance between two objects is the same. Then Pringles potato chips in a can would be mutually parallel. Well, maybe not exactly, but close enough.

How about "perpendicular?" A good start would be two objects are perpendicular if at every point of intersection the maximal angle between the two is 90 degrees. If two objects don't intersect, then say if there are natural extensions that are perpendicular then the two objects are perpendicular.

In 3D you can't have two objects that are BOTH parallel and perpendicular. But in 4D and above you can. It's perfectly normal. Consider a sphere. Choose any great circle. Take the great circle that is perpendicular to it. This circle is also parallel to the first.

Now there is a potential problem with these definitions. Consider those Pringles potato chips. Translate them further apart and they aren't parallel any more. But whatever. It's still a useful concept. If this bothers you, a less general definition of parallel can be used. Probably a good idea, but I can't be bothered.