Question

The plane $XOZ$ divides the join of $(1,-1,5)$ and $(2,3,4)$ in the ratio $\lambda :1$, then $\lambda$ is

• A. $-3$
• B. $\frac{1}{4}$
• C. $3$
• D. $\frac{1}{3}$

Answer 1

The correct option is D $\frac{1}{3}$

Given points are $(1,-1,5)$ and $(2,3,4)$

Using section formula the desired points is $(\frac{2\lambda +1}{\lambda +1},\frac{3\lambda -1}{\lambda +1},\frac{4\lambda +5}{\lambda +1})$

Since, this point lies in $XOZ$ plane then its $y$-co-ordinate should be zero.

$\Rightarrow \frac{3\lambda -1}{\lambda +1}=0$

$\Rightarrow \lambda =\frac{1}{3}$