Question

The equation of the plane which intersects the axis at A, B, C and the centroid of ΔABC is (α, β, γ) is ____ 

(A) x + y + z = 3αβγ

(B) x + y + z = 3

(C) (x/α) + (y/β) + (z/γ) = 3

(D) x + y + z = αβγ

Answer 1

The correct option (C) (x/α) + (y/β) + (z/γ) = 3

Explanation:

plane intersect in A(a, 0, 0), B(0, b, 0) and C(0, 0, c) centroid of ΔABC = [(a/3), (b/3), (c/3)] = (α, β, γ)

∴ a = 3α, b = 3β and c = 3γ

∴ (x/3α) + (y/3β) + (z/3γ) = 1

∴ equation of plane is (x/α) + (y/β) + (z/γ) = 3.