Question

Given $A(3,2,-4),B(5,4,-6)$ & $C(9,8,-10)$ are collinear. Ratio in which $B$ divides $AC$

• A. $1:2$
• B. $2:1$
• C. $-1:2$
• D. None of these

Answer 1

The correct option is A $1:2$

Given A $(3,2,-4)$

B $(5,4,-6)$

C $(9,8,-10)$

Let the ratio be $\lambda :1$

$\therefore 5=\frac{(3\times 1)+(9\times \lambda )}{\lambda +1}$

$\Rightarrow 5\lambda +5=3+9\lambda$

$\Rightarrow 4\lambda =2$

$\therefore \lambda =\frac{1}{2}\text{Hence the}Ratio=\lambda :1$

$=1:2$