Question

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

So we will consider $\lambda = \frac{2}{1},\mu = \frac{1}{3}$ and let R divide AB in the ratio v:1
$\lambda \mu v = - 1 \\ \Rightarrow 2.\dfrac{1}{3}v = - 1\therefore v = \frac{{ - 3}}{2} \\$
Sine, we got v=$\dfrac{{ - 3}}{2}$
Therefore, we can say that R divides AB externally in the ratio 3:2 as the value of $v = \dfrac{{ - 3}}{2}$