Q96 / 160 · AP EAMCET 2024 (21 May Shift 2) · Mathematics

If the plane $x-y+z+4=0$ divides the line joining the points $\mathrm{P}(2,3,-1)$ and $\mathrm{Q}(1,4,-2)$ in the ratio $l: m$, then $l+m$ is

  • A
    1
  • Correct answer
    B
    3
  • C
    -1
  • D
    4

Solution

Perpendicular distance of point $P(2,3,-1)$ from $x-y+z+4=0$ is $l=\left|\begin{array}{c} \frac{2-3-1+4}{\sqrt{3}} \end{array}\right|=\frac{2}{\sqrt{3}}$
Perpendicular distance of the point $(1,4,-2)$ from plane $\begin{aligned} & m=\left|\frac{1-4-2+4}{\sqrt{3}}\right|=\frac{1}{\sqrt{3}} \\ & \therefore \frac{l}{m}=\frac{2 / \sqrt{3}}{1 / \sqrt{3}}=\frac{2}{1} \Rightarrow l+m=2+1=3 . \end{aligned}$

Hence, the correct answer is option: 'B'.

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