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Vector Identity Rules Ax(BxC)

  1. Aug 25, 2009 #1
    1. The problem statement, all variables and given/known data

    Regarding the identity Ax(BxC)

    2. Relevant equations

    Does this identity only hold when A != B != C?
  2. jcsd
  3. Aug 25, 2009 #2
    Which identity are you referring to? Whatever the identity it would work for any vector....but of course the cross product of 2 equal vectors is zero =)
  4. Aug 25, 2009 #3
    Ah yes, I forgot the identifying portion of the identity:

    Ax(BxC) = B(A dot C) - C(A dot B)

    Same qualifying question as before. Obviously this identity does not just fall out of the sky and is the product of a process. I am wondering if the process is disrupted (invalid identity) by having A = B... it seems like it wouldn't be.
  5. Aug 25, 2009 #4
    No it wouldn't, I wonder what makes you think so?
  6. Aug 25, 2009 #5


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    It's fair to wonder, because some sources tend to be somewhat sloppy about explicitly stating hypotheses.
  7. Aug 25, 2009 #6


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    An identity holds for any choice of vectors. That's what makes it an "identity".
  8. Aug 25, 2009 #7


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    Not all identities are universal. For example,
    sin arcsin x = x​
    is only valid on the interval [itex][-\pi/2, \pi/2][/itex].
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