Mark against the correct answer in each of the following:
The equation of the plane which makes with the coordinate axes, a triangle with centroid (α, β, γ) is given by
Given: Centroid of triangle is (α, β, γ)
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 = 3α, B = 3β, C = 3γ 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 = α, b = β and c = γ
Therefore equation of required plane is