Solution
= Solution
Use the <Levi-Civita symbol> and <Einstein summation convention>. The <tensor contraction> $\epsilon_{ijk}\epsilon_{klm}=\delta_{il}\delta_{jm}-\delta_{im}\delta_{jl}$, expressed through the <Kronecker delta>, gives
$$
\bigl(a\times(b\times c)\bigr)_i=\epsilon_{ijk}a_j\epsilon_{klm}b_lc_m
=b_i a_jc_j-c_i a_jb_j.
$$
The last two contractions are <dot products>, proving the <vector triple product> identity $\boxed{a\times(b\times c)=(a\cdot c)b-(a\cdot b)c}$.