If \((\bar{a} \times \bar{b}) \times \bar{c}=-5 \bar{a}+4 \bar{b}\) and \(\bar{a} \cdot \bar{b}=3\), then the value of \(\bar{a} \times(\bar{b} \times \bar{c})\) is

\(\begin{aligned}
& (\overline{\mathrm{a}} \times \overline{\mathrm{b}}) \times \overline{\mathrm{c}}=(\overline{\mathrm{a}} \cdot \overline{\mathrm{c}}) \overline{\mathrm{b}}-(\overline{\mathrm{b}} \cdot \overline{\mathrm{c}}) \overline{\mathrm{a}} \\
& \text { But, }(\overline{\mathrm{a}} \times \overline{\mathrm{b}}) \times \overline{\mathrm{c}}=-5 \overline{\mathrm{a}}+4 \overline{\mathrm{b}} \\
\therefore \quad & -5 \overline{\mathrm{a}}+4 \overline{\mathrm{b}}=(\overline{\mathrm{a}} \cdot \overline{\mathrm{c}}) \overline{\mathrm{b}}-(\overline{\mathrm{b}} \cdot \overline{\mathrm{c}}) \overline{\mathrm{a}}
\end{aligned}\)
Comparing, we get
\(\begin{aligned}
\therefore \quad \overline{\mathrm{a}} \cdot \overline{\mathrm{c}}=4 & \\
\overline{\mathrm{a}} \times(\overline{\mathrm{b}} \times \overline{\mathrm{c}}) & =(\overline{\mathrm{a} \cdot} \cdot \overline{\mathrm{c}}) \overline{\mathrm{b}}-(\overline{\mathrm{a}} \cdot \overline{\mathrm{b}}) \overline{\mathrm{c}} \\
& =4 \overline{\mathrm{b}}-3 \overline{\mathrm{c}} \quad \ldots[\overline{\mathrm{a}} \cdot \overline{\mathrm{b}}=3 \text { (given) }]
\end{aligned}\)