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Proof involving cross products

  1. Sep 2, 2009 #1
    So I'm an engineering student and we're doing some work with tensors and indicial notation, and I came across something that I know is true but couldn't think of how to prove. I don't need it for hw or anything it's just a curiosity thing. OK, so

    Basically take a set of axes, 3 perpendicular vectors, call them A B and C
    Prove (AXC)'dot'(BXC) = 0 (ie the vectors are perpendicular, X stands for cross product)

    It seems like it should be really obvious but I can't think of how to solve it like a proof... I'm probably gonna feel like a moron when somebody answers but whatever.
     
  2. jcsd
  3. Sep 2, 2009 #2

    rock.freak667

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    If A,B and C are perpendicular.

    What vector does AxC give? What vector does BxC give? Knowing that when when you find the cross-product of two vectors, you get a vector perpendicular to the plane containing the two crossed vectors.
     
  4. Sep 2, 2009 #3
    Yeah I guess it was a stupid question I was just trying to think of how I would write it down on paper.
     
  5. Sep 2, 2009 #4

    rock.freak667

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    Well you could just write it as AxC =B and BxC=A, B.A = 0. You can probably expand (AxC).(BxC) and get it out. But that takes too much time in case you don't know what a.(bxc) equals.
     
  6. Sep 3, 2009 #5
    Since you mentioned tensors and indices, are you supposed to use the http://folk.uio.no/patricg/teaching/a112/levi-civita/index.html" [Broken]?
     
    Last edited by a moderator: May 4, 2017
  7. Sep 9, 2009 #6

    LCKurtz

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    A X C is perpendicular to the plane of A and C so is parallel to B. B X C is perpendicular to B so it is perpendicular to A X C. That's why the dot product is 0.
     
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