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# Curl of a vector using index notation Watch

1. curl (a × x )=2 a,
curl ((r^2).a) = 2(x × a),

x and a are vectors
2. (Original post by CammieInfinity)
curl (a × x )=2 a,
curl ((r^2).a) = 2(x × a),

x and a are vectors
these proofs are trivial from the basic definitions
however am I right in saying you trying to prove them using tensor notation (Einstein summation convention)?
3. (Original post by TeeEm)
these proofs are trivial from the basic definitions
however am I right in saying you trying to prove them using tensor notation (Einstein summation convention)?
I forgot to mention that r=magnitude of x

I have done the proofs normally but now we have to do it using index notation.
We have used Einstein summation convention and the kronecker to help do previous questions.
4. I don't think you've told us all of the information you have.

Is it possible that a is a constant vector??

(Ps I can't help with the index notation, I'm not good enough at it - sorry )
5. (Original post by CammieInfinity)
curl (a × x )=2 a,
curl ((r^2).a) = 2(x × a),

x and a are vectors
I'll work through the first one, because I don't really see that there's anything more to the question than just mechanical application of rules.

.

, so .

Substituting that in yields . First term is ; second term is .

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Updated: January 18, 2015
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