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Vector identities in index notation

  1. Apr 25, 2009 #1

    trv

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    1. The problem statement, all variables and given/known data

    Prove using index notation that,

    the x denoting a cross-product.

    (del x f del g)=del f x del g


    2. Relevant equations



    3. The attempt at a solution

    dif etc. denote partial derivatives.

    RHS=eijkdjfdkg

    LHS-I'm not even quite sure how to write it in index notation. Here's my attempt however.

    LHS=eijk dj (fdkg)

    But then if I write it like that, I can't tell the difference between LHS and RHS.

    --------------------------------------------------------------------------------------------------

    Also can someone check whether the following are correct,

    A.B=AiBi=AiBi

    (A x B)i=eijkAjBk
     
    Last edited: Apr 25, 2009
  2. jcsd
  3. Apr 25, 2009 #2

    dx

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    Homework Helper
    Gold Member

    Hint: εijkjkg = -εikjkjg = -εijkjkg

    Yes, that's correct.
     
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