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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](http://math.stackexchange.com/questions/27778).2011-09-29
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    Omg, duh moment! Thank you!2011-09-29
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    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]`2011-09-29
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    well, that had be true only in context of euclidean geometry @ silver2011-09-29

2 Answers 2

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

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    Nice diagram!!!2011-11-01
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As others have answered in the comments, this is only true in the plane, not in 3D space.