Question

Given that the points $P(3,2,-4)$ , $Q(5,4,-6)$ and $R(9,8,-10)$ are collinear, the ratio in which $Q$ divides $PR$ externally is

• A. 1 : 2
• B. 2 : 1
• C. 1 : 1
• D. 2 : 2

Answer 1

Answer: (A)

Let $Q$ divides $PR$ externally in $K:1$

By external section formula, we get
$5=\frac{9\times K-1\times 3}{K-1}$
$\Rightarrow 5K-5=9K-3$
$\Rightarrow 5K-9K=-3+5$
$\Rightarrow -4K=2$
$\Rightarrow K=-\frac{2}{4}$
$\Rightarrow K=-\frac{1}{2}$
Hence, $Q$ divides $PR$ in the ratio $1:2$ (externally).