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I'm asked to prove the following identity, using index notation:

$(\nabla\times A)\times A=A \cdot\nabla A - \nabla(A \cdot A)$

However, when I work it out, I find that the actual solution should be:

$(\nabla\times A)\times A=A \cdot\nabla A - \frac{1}{2}\nabla(A \cdot A)$

Am I missing something, or is the book wrong?

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    Here, A is a vector, of course.2012-10-09

4 Answers 4