Find the equation of a plane which meets the axes in A, B and C, given that the centroid of the triangle ABC is the point (α, β, γ).

It is given in the question that the plane meets the axes in A, B, C

So now let us assume that A = (a, 0, 0), B = (0, b, 0) and C = (0, 0, c)

Given that the centroid is and we know the formula of the centroid of

So,

So we have now

We know that, The equation of the plane whose intercepts on the coordinate axes a, b, c is given by the equation

Now substitute a, b, c

We get

so this is the equation.