VC3.17

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Given,V=e^{{xyz}}(i+j+k)\,

Hence {\mathrm  {curl}}F={\begin{vmatrix}i&j&k\\{\frac  {\partial }{\partial x}}&{\frac  {\partial }{\partial y}}&{\frac  {\partial }{\partial z}}\\e^{{xyz}}&e^{{xyz}}&e^{{xyz}}\end{vmatrix}}\,

=i[{\frac  {\partial e^{{xyz}}}{\partial y}}-{\frac  {\partial e^{{xyz}}}{\partial z}}]-j[{\frac  {\partial e^{{xyz}}}{\partial x}}-{\frac  {\partial e^{{xyz}}}{\partial z}}]+k[{\frac  {\partial e^{{xyz}}}{\partial x}}-{\frac  {\partial e^{{xyz}}}{\partial y}}]\,

=i(xze^{{xyz}}-xye^{{xyz}})-j(yze^{{xyz}}-xye^{{xyz}})+k(yze^{{xyz}}-xze^{{xyz}})\,

=[x(z-y)i+y(x-z)j+z(y-x)k]e^{{xyz}}\,

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