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If the foot of the perpendicular from $(0,0,0)$ to a plane is $(1,2,3)$, then the equation of the plane is
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Verified Answer
The correct answer is:
$x+2 y+3 z=14$
The equation of a plane passing through $(1,2,3)$ is
$a(x-1)+b(y-2)+c(z-3)=0$
$\begin{aligned} & \text { Also, }(a, b, c)=(1-0,2-0,3-0) \\ & -(1,2,3) \\ & \therefore 1(x-1)+2(y-2)+3(z-3)=0 \\ & \Rightarrow \quad x+2 y+3 z-1-4-9=0 \\ & \Rightarrow \quad x+2 y+3 z=14 \\ & \end{aligned}$
$a(x-1)+b(y-2)+c(z-3)=0$
$\begin{aligned} & \text { Also, }(a, b, c)=(1-0,2-0,3-0) \\ & -(1,2,3) \\ & \therefore 1(x-1)+2(y-2)+3(z-3)=0 \\ & \Rightarrow \quad x+2 y+3 z-1-4-9=0 \\ & \Rightarrow \quad x+2 y+3 z=14 \\ & \end{aligned}$
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