Q101 / 160 · TS EAMCET 2023 (13 May Shift 1) · Mathematics

$(1,-2,1)$ is a point on a plane $\pi$ and $\pi$ is parallel to the plane $x-y-z=0$. If the equation of $\pi$ is $a x+b y+c z-2$ $=0$, then $b-2 c=$

  • A
    $-\mathrm{a}$
  • B
    $2 a$
  • C
    $-2 a$
  • Correct answer
    D
    a

Solution

$\because \quad$ Plane is parallel to $x-y-z=0$ $\therefore$ Equation of plane is $$ \begin{aligned} & \left(x-x_1\right)-\left(y-y_1\right)-\left(z-z_1\right)=0 \\ \therefore \quad & (x-1)-(y+2)-(z-1)=0 \\ & x-y-z-2=0 \\ \therefore \quad & a=1, b=-1, c=-1 \\ & b-2 c=-1-2(-1)=1=a \end{aligned} $$

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

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