Question

Show that if $P$ divides $BC$ in ratio $2:1$ and $Q$ divides $CA$ in ratio $1:3$ then $R$ divides $AB$ in the ratio $3:2$ externally.

Answer 1

Given $\lambda =2,\mu =\frac{1}{3}$ and let $R$ divide $AB$ in the ratio $v:1$.
Then by part (b) $\lambda \mu v=-1$ $2.\frac{1}{3}v=-1$ $\therefore v=-\frac{3}{2}$
$\therefore R$ divides in the ratio $3:2$ externally, as $v=-\frac{3}{2}$