Sol. let the equation of plane is – …..(i)

where a, b, c are variables

This plane meets x, y and z axes at A (a,0,0), B(0,b,0) and C(0,0,c). Let ( α , β , γ ) be the co-ordinates of the centroid of triangle ABC. Then –

α = a/3, β = b/3, γ = c/3 …….(ii)

The distance of this plane from origin is = 3p,

therefore-

3p = length of perpendicular from (0, 0, 0) to plane (i) is –

⇒ ………(iii)

from (ii), we have –

a = 3 α , b = 3 β , c = 3 γ

Now, putting the values of a, b, c in (iii), we have

so the locus of ( α , β , γ ) is –

∴ x –2 + y –2 + z –2 = p –2