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If a plane meets the co-ordinate axes at $A, B$ and $C$ such that the centroid of the triangle is $(1,2$, 4) then the equation of the plane is
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Verified Answer
The correct answer is:
$4 x+2 y+z=12$
Given, plane meets the co-ordinate axes at $A(a, 0,0), B(0, b, 0) C(0,0, c)$
$\begin{aligned}
& \quad \equiv\left(\frac{a}{3}, \frac{b}{3}, \frac{c}{3}\right)=(1,2,4) \\
& \therefore \text { Centroid } \\
& \Rightarrow a=3, b=6, c=12
\end{aligned}$
Hence, equation of required plane is, $\frac{x}{3}+\frac{y}{6}+\frac{z}{12}=1$
$\Rightarrow 4 x+2 y+z=12 \text {. }$
$\begin{aligned}
& \quad \equiv\left(\frac{a}{3}, \frac{b}{3}, \frac{c}{3}\right)=(1,2,4) \\
& \therefore \text { Centroid } \\
& \Rightarrow a=3, b=6, c=12
\end{aligned}$
Hence, equation of required plane is, $\frac{x}{3}+\frac{y}{6}+\frac{z}{12}=1$
$\Rightarrow 4 x+2 y+z=12 \text {. }$
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