Q98 / 160 · AP EAMCET 2024 (22 May Shift 1) · Mathematics

If the perpendicular distance from $(1,2,4)$ to the plane $2 x+2 y-z+k=0$ is 3 , then $k=$

  • A
    4
  • Correct answer
    B
    7
  • C
    9
  • D
    19

Solution

$\begin{aligned} & 2 x+2 y-z+k=0, P(1,2,4) \\ & p=\left|\frac{2(1)+(2)(2)-(4)+k}{\sqrt{4+4+1}}\right| \Rightarrow 3=\left|\frac{2+k}{3}\right| \Rightarrow k=7 .\end{aligned}$

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

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