Vector identities in index notation

[trv]

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

d_if etc. denote partial derivatives.

RHS=e^ijkd_jfd_kg

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

LHS=e^ijk d_j (fd_kg)

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

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Also can someone check whether the following are correct,

A.B=A_iBⁱ=AⁱB_i

(A x B)_i=e_ijkA_jB_k

 

[dx]

Hint: ε^ijk∂_j∂_kg = -ε^ikj∂_k∂_jg = -ε^ijk∂_j∂_kg

Also can someone check whether the following are correct,

A.B=A_iBⁱ=AⁱB_i

(A x B)_i=e_ijkA_jB_k

Yes, that's correct.