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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.

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Hint: Apply section formula and solve this question.

Given that point P divides BC in the ratio 2:1 and Q divides CA in the ratio 1:3 and R divides AB externally in the ratio 3:2
So we will consider $\lambda = \frac{2}{1},\mu = \frac{1}{3}$ and let R divide AB in the ratio v:1
So,from section formula we can write this as equal to
$
  \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 $v = \dfrac{{ - 3}}{2}$

Note: Always apply the relevant section formula in accordance to the data which is given, here since we have been given with both internal and external division ,we have applied the respective formula and solved it

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