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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