Let \(\overline{\mathrm{a}}, \overline{\mathrm{b}}\) and \(\overline{\mathrm{c}}\) be three unit vectors such that \(\overline{\mathrm{a}} \times(\overline{\mathrm{b}} \times \overline{\mathrm{c}})=\frac{\sqrt{3}}{2}(\overline{\mathrm{b}}+\overline{\mathrm{c}})\). If \(\overline{\mathrm{b}}\) is not parallel to \(\overline{\mathrm{c}}\), then the angle between \(\bar{a}\) and \(\bar{b}\) is

\(
\begin{aligned}
& \overline{\mathrm{a}} \times(\overline{\mathrm{b}} \times \overline{\mathrm{c}})=\frac{\sqrt{3}}{2}(\overline{\mathrm{b}}+\overline{\mathrm{c}}) \\
& \Rightarrow(\overline{\mathrm{a}} \cdot \overline{\mathrm{c}}) \overline{\mathrm{b}}-(\overline{\mathrm{a}} \cdot \overline{\mathrm{b}}) \overline{\mathrm{c}}=\frac{\sqrt{3}}{2} \overline{\mathrm{b}}+\frac{\sqrt{3}}{2} \overline{\mathrm{c}}
\end{aligned}
\)
On comparing, we get
\(
\begin{aligned}
& \overline{\mathrm{a}} \cdot \overline{\mathrm{c}}=\frac{\sqrt{3}}{2} \text { and } \overline{\mathrm{a}} \cdot \overline{\mathrm{b}}=-\frac{\sqrt{3}}{2} \\
& \Rightarrow|\overline{\mathrm{a}}||\overline{\mathrm{b}}| \cos \theta=-\frac{\sqrt{3}}{2} \\
& \Rightarrow \cos \theta=-\frac{\sqrt{3}}{2} \\
& \Rightarrow \theta=\frac{5 \pi}{6}
\end{aligned}
\)