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