Q208 / 270 · NDA 2012 (Phase 2) · Mathematics

What is the equation to the plane through $(1,2,3)$ parallel to $3 x+4 y-5 z=0$ ?

  • A
    $3 x+4 y+5 z+4=0$
  • B
    $3 x+4 y-5 z+14=0$
  • Correct answer
    C
    $3 x+4 y-5 z+4=0$
  • D
    $3 x+4 y-5 z-4=0$

Solution

Let equation of plane parallel to $3 x+4 y-5 z=0$ is $3 x+4 y-5 z+\lambda=0$ $\because$ it passes through $(1,2,3)$ $\therefore 3(1)+4(2)-5(3)+\lambda=0$ $\begin{aligned} \Rightarrow & & 3+8-15+\lambda & =0 \\ \Rightarrow & & \lambda & =4\end{aligned}$ $\therefore$ equation of plane is $3 x+4 y-5 z+4=0$.

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

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