Let the ratio be $\lambda:1$

According to section formula, the coordinates of R is given by $(\large\frac{5\lambda+3}{\lambda+1},\frac{4\lambda+2}{\lambda+1},\frac{-6\lambda-4}{\lambda+1})$

$\Rightarrow\:\large\frac{5\lambda+3}{\lambda+1}$$=9$

$\Rightarrow\:\lambda=-\large\frac{3}{2}$

$\therefore$ $R$ divides $PQ$ in ratio $3:2\:externally$ (since $\lambda$ is negative.)