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A plane $\pi$ passing through the point $(1,1,1)$ is perpendicular to the line joining the points $(6,3,2)$ and $(1,-4,-9)$. If $a x+b y+c z-23=0$ is the equation of the plane $\pi$ then $\mathrm{a}+\mathrm{b}-\mathrm{c}=$
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The correct answer is:
1
D.R. of line joining points $(6,3,2)$ and $(1,-4,-9)$ is $(5,7,11)$
$\therefore \quad$ Equation of plane is
$$
\begin{aligned}
& 5(x-1)+7(y-1)+11(z-1)=0 \\
\Rightarrow & 5 x+7 y+11 z-23=0 \\
\therefore \quad & a=5, b=7, c=11 \\
\Rightarrow & a+b-c=5+7-11=1 .
\end{aligned}
$$
$\therefore \quad$ Equation of plane is
$$
\begin{aligned}
& 5(x-1)+7(y-1)+11(z-1)=0 \\
\Rightarrow & 5 x+7 y+11 z-23=0 \\
\therefore \quad & a=5, b=7, c=11 \\
\Rightarrow & a+b-c=5+7-11=1 .
\end{aligned}
$$
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