Question

Ratio in which the $xy-$plane divides the join of $(1,2,3)$ and $(4,2,1)$ is

• A. $3:1$ internally
• B. $3:1$ externally
• C. $1:2$ internally
• D. $2:1$ externally

Answer 1

The correct option is B $3:1$ externally

Points $A(1,2,3),B(4,2,1)$

$x-y$ plane $\Rightarrow z=0$

$\therefore$ lines containing $A,B$ is $\frac{x-1}{3}=\frac{y-2}{0}=\frac{z-3}{-2}$

point of intersection of line and $xy$ plane is $(\frac{11}{2},2,0)$

$\therefore (\frac{4\lambda +1}{\lambda +1},\frac{2\lambda +2}{\lambda +1},\frac{\lambda +3}{\lambda +1})=(\frac{11}{2},2,0)\Rightarrow \lambda =-3$

Answer $\left(B\right)$