VC5.29

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Let V be the volume enclosed by S.By definition,

{\mathrm  {div}}F={\frac  {\partial }{\partial x}}(ax)+{\frac  {\partial }{\partial y}}(by)+{\frac  {\partial }{\partial z}}(cz)=a+b+c\,

Hence,by divergence theorm,we have

\iint _{S}F\cdot ndS=\iiint _{V}{\mathrm  {div}}FdV=\iiint _{V}(a+b+c)dV\,,by (1)

=(a+b+c)V={\frac  {4}{3}}\pi (a+b+c)\,

V=Volume of the given sphere of unit radius={\frac  {4}{3}}\pi (1)^{3}={\frac  {4\pi }{3}}\,

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