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Vector identities in index notation

  • Thread starter trv
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  • #1
trv
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Homework Statement



Prove using index notation that,

the x denoting a cross-product.

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


Homework Equations





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:

Answers and Replies

  • #2
dx
Homework Helper
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Hint: εijkjkg = -εikjkjg = -εijkjkg

Also can someone check whether the following are correct,

A.B=AiBi=AiBi

(A x B)i=eijkAjBk
Yes, that's correct.
 

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