$$\begin{gathered} \mathrm{Given}, \mathrm{a} \mathrm{is} \mathrm{perpendicular} \mathrm{to} \mathrm{both} \mathrm{b} \mathrm{and} \mathrm{c} \\ \mathrm{Then}, \mathrm{a} . \mathrm{b} = 0 \mathrm{and} \mathrm{a} . \mathrm{c} = 0 ...\left(\mathrm{i}\right) \\ \mathrm{Now}, \mathrm{we} \mathrm{have} \\ \mathrm{a} \times \left(\mathrm{b} \times \mathrm{c}\right) = \left(\mathrm{a} . \mathrm{c}\right)\mathrm{b} - \left(\mathrm{a} . \mathrm{b}\right)\mathrm{c} \\ = \left(0\right)\mathrm{b} - \left(0\right)\mathrm{c} \\ = 0 - 0 = 0 \end{gathered}$$