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the following problem is in the arfken/weber textbook and was also on a practice exam for my mathematical methods course:

Verify that

[tex]

\mathbf{A} \times (\nabla \times \mathbf{A}) = \frac{1}{2} \nabla(A^2) - (\mathbf{A} \cdot \nabla)\mathbf{A}.

[/tex]

i used the BAC-CAB rule, but i don't get the factor of 1/2.

the solutions booklet that came with the textbook very tersely explains, "the factor of 1/2 occurs because the del only operates on one of the A's."

i would very much appreciate an explanation that is perhaps more informative than this one sentence blurb! :tongue:

thank you.

Verify that

[tex]

\mathbf{A} \times (\nabla \times \mathbf{A}) = \frac{1}{2} \nabla(A^2) - (\mathbf{A} \cdot \nabla)\mathbf{A}.

[/tex]

i used the BAC-CAB rule, but i don't get the factor of 1/2.

the solutions booklet that came with the textbook very tersely explains, "the factor of 1/2 occurs because the del only operates on one of the A's."

i would very much appreciate an explanation that is perhaps more informative than this one sentence blurb! :tongue:

thank you.

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