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Transitive Property with Orthogonal Vectors?

  1. Apr 20, 2010 #1
    1. The problem statement, all variables and given/known data

    Let x1, x2, and x3 be vectors in R^3. If x1 is orthogonal to x2 and x2 is orthogonal to x3, is it necessarily true that x1 is orthogonal to x3?

    2. Relevant equations

    I know that if x1 is orthogonal to x2 and x2 is orthogonal to x3, then...


    3. The attempt at a solution

    I think that the answer would be no. I can imagine it geometrically, but I'm not sure how I would prove this algebraically.

    I would obviously have to prove that (x1)^T*x3 would ALWAYS have to equal 0 if it the statement was necessarily true... but I'm not sure how to go about doing that...

    I'm completely stuck. I would greatly appreciate your help!
  2. jcsd
  3. Apr 20, 2010 #2


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    Homework Helper

    Try to think of an example.
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