We were asked to prove the Chandrasekhar-Wentzel lemma using any method different to the one given in Wikipedia. $$\oint_cr \times (dr \times n) = -\iint_s(r \times n)\nabla\cdot n ds $$
I started this by expanding the LHS using the properties of the cross product. $$\oint_cr \times (dr \times n) = \oint_c(r \cdot n)dr - \oint_c(r \cdot dr)n$$
Since $r \cdot n$ is a scalar I can convert it to a surface integral as, $$ \oint_c(r \cdot n)dr = -\iint_s\nabla(r \cdot n) \times ds $$
I can not think of a way to going further. What can I do from here on? Or is there another way for this (except for the one in wikipedia).