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If a variable plane, at a distance of 3 units from the origin, intersects the coordinate axes at A, B and C, then the locus of the centroid of $Δ A B C$ is

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1x2+1y2+1z2=1

1x2+1y2+1z2=3

1x2+1y2+1z2=19

1x2+1y2+1z2=9

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detailed solution

Correct option is A

A(a,0,0)B(0,b,0)C(0,0,c)⇒Gx1,y1,z1=a3,b3,c3Equation of the plane is xa+yb+zc=1; x3x1+y3y1+z3z1=1P=|d|a2+b2+c2,3=119x12+19y12+19z12

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If a variable plane, at a distance of 3 units from the origin, intersects the coordinate axes at A, B and C, then the locus of the centroid of ΔABC is

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If a variable plane, at a distance of 3 units from the origin, intersects the coordinate axes at A, B and C, then the locus of the centroid of $Δ A B C$ is