Stock`s theorem $$\oint\limits_C {{\bf{a}} \cdot {\bf{dr}}} = \iint\limits_S {\nabla \times {\bf{a}}\, \cdot {\bf{n}}dA}$$
Substituting ${\bf{a}} = {\bf{f}} \times {\bf{c}}$ we find that $$\oint\limits_C {{\bf{dr}} \times {\bf{f}}} = \iint\limits_S {\left( {{\bf{n}} \times \nabla \,} \right) \times {\bf{f}}dA}$$ since ${\bf{n}} \cdot \left( {\nabla \times \left( {{\bf{f}} \times {\bf{c}}} \right)} \right) = {\bf{c}} \cdot \left( {\left( {{\bf{n}} \times\nabla } \right) \times {\bf{f}}} \right) % MathType!MTEF!2!1!+- % feaagKart1ev2aaatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn % hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYfdmGievaebbnrfi % fHhDYfgasaacH8srps0lbbf9q8WrFfeuY-Hhbbf9v8qqaqFr0xc9pk % 0xbba9q8WqFfea0-yr0RYxir-Jbba9q8aq0-yq-He9q8qqQ8frFve9 % Fve9Ff0dmeaabaqaciGacaGaaeqabaWaaeaaeaaakeaacaWHUbGaey % yXIC9aaeWaaeaadaWhcaqaaiabgEGirdGaay51GaGaey41aq7aaeWa % aeaacaWHMbGaey41aqRaaC4yaaGaayjkaiaawMcaaaGaayjkaiaawM % caaiabg2da9iaahogacqGHflY1daqadaqaamaabmaabaGaaCOBaiab % gEna0oaaFiaabaGaey4bIenacaGLxdcaaiaawIcacaGLPaaacqGHxd % aTcaWHMbaacaGLOaGaayzkaaaaaa!55F5! $
I can`t prove last equation, please help,
c is constant vector, n is unit vector, a and f are vector functions