Parallel Worlds (really just with lines and planes)

Question

Can someone help me understand/visualize why the two true/false questions below are false? I thought they were true.

True or False 2. Two lines perpendicular to a third line are parallel. CORRECT ANSWER: false

I'll respond quickly!

EDIT: Deleted one because I figured it out after typing it in!

"Two lines perpendicular to a third line are parallel." - in the plane, true; in space, false. See for instance this related question.
If you have Mathematica: Graphics3D[{Line[{{0, 2, 1}, {0, -2, 1}}], Line[{{2, 0, -1}, {-2, 0, -1}}], Line[{{0, 0, 2}, {0, 0, -2}}]}, Boxed -> False]
well, that had be true only in context of euclidean geometry @ silver

Emmad Kareem · Accepted Answer · 2011-10-29 14:21:12Z

up vote 0 down vote accepted

To clarify here is a picture in 3-D enter image description here

answered Oct 29 '11 at 14:21

Emmad Kareem
1,6371311

	Nice diagram!!! – user13327 Nov 1 '11 at 20:28
	Thanks for your comment. – Emmad Kareem Nov 1 '11 at 20:51

user13327 · Answer 2 · 2011-09-29 05:28:14Z

up vote 2 down vote

As others have answered in the comments, this is only true in the plane, not in 3D space.

answered Sep 29 '11 at 5:28

user13327

2 Answers