VC3.39

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Using identity \mathrm{div}(f\times g)=g\cdot\mathrm{curl}f-f\cdot\mathrm{curl}g\,, we get

\mathrm{div}(A\times r)=r\cdot\mathrm{curl}A-A\cdot\mathrm{curl}r\,

=r\cdot\mathrm{curl}A-A(0)\, [Since \mathrm{curl}r=0\,]

Thus,\mathrm{div}(A\times r)=r\cdot\mathrm{curl}A\,


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