Question

Points $A(3,2,4),B\left(\frac{33}{5},\frac{28}{5},\frac{38}{5}\right)$ and $C(9,8,10)$ are given. The ratio in which $B$ divides $AC$ is

• A. 5 : 3
• B. 2 : 1
• C. 1 : 3
• D. 3 : 2

Answer 1

Answer: (D)

Let $B\left(\frac{33}{5},\frac{28}{5},\frac{38}{5}\right)$ divides $\overline{AC}$ in the ratio $k:1$,
where $A(3,2,4)$ an $dC(9,8,10)$

Now, $\frac{9k+3}{k+1}=\frac{33}{5}$
$\Rightarrow 45k+15=33k+33$
$\Rightarrow 12k=18$
$\therefore k=\frac{3}{2}...(i)$
and $\frac{8k+2}{k+1}=\frac{28}{5}$
$\Rightarrow 40k+10=28k+28$
$\Rightarrow 12k=18$
$\Rightarrow k=\frac{3}{2}...(ii)$
and $\frac{10k+4}{k+1}=\frac{38}{5}$
$\Rightarrow 50k+20=38k+38$
$\Rightarrow 12k=18$
$\Rightarrow k=\frac{3}{2}...(iii)$
From Eqs. (i), (ii) and (iii), we get
$k=\frac{3}{2}$
Now, $k:1=\frac{3}{2}:1=3:2$