Given, plane meets the coordinate axes at A, B and C. Let the plane meets the coordinate axes at the points A(a,0,0),B(0,b,0),C(0,0,c) The equation of plane is
x
a
+
y
b
+
z
c
=1 ...(i) Centroid formula says, x=
x1+x2+x3
3
,y=
y1+y2+y3
3
, z=
z1+z2+z3
3
Centroid of ΔABC=(
a
3
,
b
3
,
c
3
) Given centroid =(1,2,3) ⇒ (
a
3
,
b
3
,
c
3
) Therefore, a=3,b=6 and c=9 Put the value of a,b and c in equation of plane (i). we get