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If the foot of the perpendicular drawn from $(0,0,0)$ to a plane is $(1,2,3)$, then equation of the plane is
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Verified Answer
The correct answer is:
$x+2 y+3 z=14$
$\because$ Foot of perpendicular lies on the plane. So, the
equation of plane is
$a(x-1)+b(y-2)+c(z-3)=0$ ...(i)
$\because \quad$ Line joining $(0,0,0)$ and $(1,2,3)$ is perpendicular to the plane (i).
$\therefore \quad a=1-0=1, b=2-0=2, c=3-0=3$
So, equation (i) reduces to
$\begin{aligned} & 1(x-1)+2(y-2)+3(z-3)=0 \\ & \Rightarrow \quad x+2 y+3 z=14\end{aligned}$
equation of plane is
$a(x-1)+b(y-2)+c(z-3)=0$ ...(i)
$\because \quad$ Line joining $(0,0,0)$ and $(1,2,3)$ is perpendicular to the plane (i).
$\therefore \quad a=1-0=1, b=2-0=2, c=3-0=3$
So, equation (i) reduces to
$\begin{aligned} & 1(x-1)+2(y-2)+3(z-3)=0 \\ & \Rightarrow \quad x+2 y+3 z=14\end{aligned}$
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