Question

If $A(3,2,-4),B(5,4,-6)$ and $C(9,8,-10)$ are three collinear point then point $C$ divides $AB$

• A. internally in the ratio 2 : 3
• B. externally in the ratio 3 : 2
• C. internally in the ratio 3 : 2
• D. externally in the ratio 2 : 3

Answer 1

Answer: (B)

Let $C$ divide $AB$ in the ratio $\lambda :1$. Then
$C\equiv \left(\frac{5\lambda +3}{\lambda +1},\frac{4\lambda +2}{\lambda +1},\frac{-6\lambda -4}{\lambda +1}\right)=(9,8-10)$
Comparing the coordinates, we get
$5\lambda +3=9\lambda +9$ or $4\lambda =-6$
$\therefore \lambda =-3/2$
Also from $4\lambda +2=8\lambda +8$ and $-6\lambda -4=-10\lambda -10$, we get the same value of $\lambda$.