Q. 285.0( 1 Vote )

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

A. αx + βy + γz = 1

B. αx + βy + γz = 3

C.

D.

Answer :

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

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