Question

Given that $A(3,2,-4),B(5,4-6)$ and $C(9,8,-10)$ are collinear. Ratio in which $B$ divides $AC$ is $1:m$. The value of $m$ is

• A. 2
• B. 3
• C. 4
• D. 5

Answer 1

Answer: (A)

Suppose B divides $AC$ in the ratio $\lambda :1$.
$\therefore B=\left(\frac{9\lambda +3}{\lambda +1},\frac{8\lambda +2}{\lambda +1},\frac{-10\lambda -4}{\lambda +1}\right)=(5,4,-6)$
$\Rightarrow \frac{9\lambda +3}{\lambda +1}=5,\frac{8\lambda +2}{\lambda +1}=4,\frac{-10\lambda -4}{\lambda +1}=-6$
$\Rightarrow \lambda =\frac{1}{2}$
So, required ratio is $1:2$.