Mark against the A. x + 2y + 4z = 6

B. 4x + 2y + z = 12

C. x + 2y + 4z = 7

D. 4x + 2y + z = 7

Given: Centroid of ∆ABC is (1, 2, 4)

To find: Equation of plane.

Formula Used: Equation of plane is where (x, y, z) is a point on the plane and a, b, c are intercepts on x-axis, y-axis and z-axis respectively.

Centroid of a triangle

Explanation:

Let the equation of plane be

… (1)

Therefore, A = 3a, B = 3b, C = 3c where (a, b, c) is the centroid of the triangle with vertices (A, 0, 0), (0, B, 0) and (0, 0, C)

Substituting in (1),

Here a = 1, b = 2 and c = 4

Multiplying by 12,

4x + 2y + z = 12

Therefore equation of required plane is 4x + 2y + z = 12