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If a plane meets the equations axes at `A ,Ba n dC` such that the centroid of the triangle is `(1,2,4),` then find the equation of the plane.

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Let the plane meet the coordinates axes at `A(a, 0, 0), B(0, b, 0), and C(0, 0, c).` Then,
`" "a=3, b=6, c=12`.
Hence, the equation of required plane is `(x)/(3)+(y)/(6)+(z)/(12)=1 or 4x+2y+z=12`
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