[QUE/ME-02010]

Using definition of Levi-Civita  epsilon symbol and Kronecker delta symbol to show that \begin{equation}\epsilon_{i\,j\,k}\,\epsilon_{k\,\ell\,m}\ =\ (\,\delta_{i\ell}\,\delta_{jm}\,-\,\delta_{im}\,\delta_{j\ell}) \end{equation} Use this  identity to prove that \begin{equation}\vec{A}\times(\vec{B}\times\vec{C})=(\vec{A}\cdot\vec{C})\vec{B} -(\vec { A } \cdot\vec{B})\vec{C}.\end{equation}