VC4.13

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Along the curve C,we have r=a\cos ti+b\sin tj+ctk,r=xi+yj+zk\,

Hence x=a\cos t,y=b\sin t,z=ct\, --(1)

Therefore \int _{{C}}F\cdot \,dr=<math>\int _{{C}}(yzi+zxj+xyk)\cdot (dxi+dyj+dzk)\,

=\int _{{C}}(yzdx+zxdy+xydz)\,

=\int _{{C}}d(xyz)=[xyz]_{{t=0}}^{{t={\frac  {\pi }{2}}}}\,

=[(a\cos t)(b\sin t)(ct)]_{{0}}^{{{\frac  {\pi }{2}}}}\,, by using (1)

=abc[t\cos t\sin t]_{{0}}^{{{\frac  {\pi }{2}}}}=abc(0-0)=0\,

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