Given that \(\bar{a}+\bar{b}+\bar{c}=0\) Squaring both the sides \[\] \(|\bar{a}|^{2}+|\bar{b}|^{2}+|\bar{c}|^{2}+2 \bar{a} \cdot \bar{b}+2 \bar{b} \cdot \bar{c}+2 \bar{a} \cdot \bar{c}=0\) \[\] \(\Rightarrow \bar{a} \cdot \bar{b}+\bar{b} \cdot \bar{c}+\bar{c} \cdot \bar{a}=-\frac{3}{2}\) \[\] Choice (D)\[\]