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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!

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"Two lines perpendicular to a third line are parallel." - in the plane, true; in space, false. See for instance this related question. – J. M. Sep 29 '11 at 1:52
Omg, duh moment! Thank you! – user13327 Sep 29 '11 at 1:56
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] – J. M. Sep 29 '11 at 2:01
well, that had be true only in context of euclidean geometry @ silver – Bhargav Sep 29 '11 at 2:07

2 Answers 2

up vote 1 down vote accepted

To clarify here is a picture in 3-Denter image description here

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

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

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