VC5.27

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Here {\mathrm  {div}}F={\frac  {\partial }{\partial x}}(ax)+{\frac  {\partial }{\partial y}}(by)+{\frac  {\partial }{\partial z}}(cz)=a+b+c\, --(1)

Therefore,by the divergence theorm,we have

\iint _{F}F\cdot ndS=\iiint _{V}{\mathrm  {div}}FdV\, V being volume enclosed by S

=\iiint _{V}(a+b+c)dV\,,using (1)

=(a+b+c)V={\frac  {4}{3}}\pi (a+b+c)\, Since V=volume of a sphere of unit radius={\frac  {4}{3}}\pi (1)^{3}={\frac  {4}{3}}\pi \,

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