Mark against the correct answer in each of the following:
If a plane meets the coordinate axes in A, B and C such that the centroid of ∆ABC is (1, 2, 4), then the equation of the plane is
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