A plane meets the co - ordinate axes at A, B, C such that the centroid of ΔABC is the point (a, b, c).

Let, the co - ordinates of the point A (α, 0, 0), B (0, β, 0) and C (0, 0, γ).

According to the centroid formula,

We know the intercept form of a plane is given as,

if the plane makes intercepts at (p, 0, 0), (0, q, 0) and (0, 0, r) with the x - , y - and z - axes respectively.

Here, p=α=3a, q=β=3b and r=γ=3c

So, the equation of the plane is,

Equation of the given plane is

On comparing, we get, k=3.