If $\overline{\mathrm{c}}=3\overline{\mathrm{a}}+4\overline{\mathrm{b}}\text{ and }2\overline{\mathrm{c}}=\overline{\mathrm{a}}-3\overline{\mathrm{b}}$, then 

$\begin{array}{l}\overline{\mathrm{c}}=3\overline{\mathrm{a}}+4\overline{\mathrm{b}}\mathrm{\&}2\overline{\mathrm{c}}=\overline{\mathrm{a}}-3\overline{\mathrm{b}}\Rightarrow \overline{\mathrm{a}}=3\overline{\mathrm{b}}+2\overline{\mathrm{c}}\\ \therefore \overline{\mathrm{c}}=3(3\overline{\mathrm{b}}+2\overline{\mathrm{c}})+4\overline{\mathrm{b}}\Rightarrow \overline{\mathrm{c}}=13\overline{\mathrm{b}}+6\overline{\mathrm{c}}\\ \Rightarrow -5\overline{\mathrm{c}}=13\overline{\mathrm{b}}\Rightarrow \overline{\mathrm{c}}=\frac{-13}{5}\overline{\mathrm{b}}\Rightarrow \overline{\mathrm{c}}\mathrm{\&}\overline{\mathrm{b}}\end{array}$ 
$$\begin{gathered} are collinear vectors and direction of \overline{ c} is opposite to that of \overline{b} \\ \left|\overline{\mathrm{c}}\right|=\left|\frac{-13}{5}\overline{\mathrm{b}}\right|=\frac{13}{5}\left|\overline{\mathrm{b}}\right|\Rightarrow \left|\overline{\mathrm{c}}\right|>2\left|\overline{\mathrm{b}}\right| \end{gathered}$$