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# How can lines be both perpendicular and skew? Watch

1. I was doing the OCR January 2008 C4 paper, and question 5 asked me to prove that two vectors were perpendicular, and then also prove that they're skew.

I managed to do both, by showing that a-dot-b was equal to zero, and then by showing that the lines are neither parallel nor intersecting... but I don't understand it.

How can two lines that don't meet be perpendicular?
2. (Original post by dendodge)

How can two lines that don't meet be perpendicular?
Look at the room you are in

Look at a line where the wall A meets the floor

Look at the line where Wall B meets Wall C

Does that help
3. Imagine translating one line (so not rotating it at all) until it intersects the other line, and then calculating the angle between them.
4. Oh, that makes sense. It was a lot less complicated than I was trying to make it

Thank you!
5. Firstly, be careful when talking about vectors and then referring to lines - they are related but they aren't the same thing.

Secondly,to see how two lines in 3 dimensional space can be perpendicular yet not meet, do the following:

1. Cross your two index fingers so that they are perpendicular to each other.
2. Preserving the angle between your fingers leave one in place and move the other back towards your body.
3. The lines passing through your two index fingers are perpendicular yet they don't meet.

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Updated: April 12, 2013
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