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 $A C$ 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 $\overline{A C}$ in the ratio $k: 1$,
where $A(3,2,4)$ an $d C(9,8,10)$

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