If $\mathrm{k}\overline{\mathrm{a}} = 3 \overline{\mathrm{b}} + 2 \overline{\mathrm{c}}, \overline{\mathrm{a}} = -2 \overline{\mathrm{b}} + 5\overline{\mathrm{c}}$ and if b and c have opposite direction, then

$$\begin{gathered} \overline{\mathrm{a}}=\frac{3\overline{\mathrm{b}}+2\overline{\mathrm{c}}}{\mathrm{k}} \overline{\mathrm{a}}=-2\overline{\mathrm{b}}+5\overline{\mathrm{c}} \\ 3\overline{\mathrm{b}}+2\overline{\mathrm{c}}=-2\mathrm{k}\overline{\mathrm{b}}+5\mathrm{k}\overline{\mathrm{c}} \\ (3+2\mathrm{k})\mathrm{b}=(5\mathrm{k}-2)\overline{\mathrm{c}} \Rightarrow \overline{\mathrm{b}}=\frac{5\mathrm{k}-2}{3+2\mathrm{k}}=\overline{\mathrm{c}} \\ \frac{5\mathrm{k}-2}{2\mathrm{k}+3}<0 \Rightarrow (5\mathrm{k}-2) (2\mathrm{k}+3)<0 \\ \Rightarrow \mathrm{k}\in \left(\raisebox{1ex}{$-3$}\!\left/ \!\raisebox{-1ex}{$2$}\right., \raisebox{1ex}{$2$}\!\left/ \!\raisebox{-1ex}{$5$}\right.\right) \end{gathered}$$