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 byA. αx + βy + γz = 1B. αx + βy + γz = 3C. D.

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

Rate this question :

How useful is this solution?
We strive to provide quality solutions. Please rate us to serve you better.
RELATED QUESTIONS :

Find the coordinate of the point P where the line through and crosses the plane passing through three points and Also, find the ratio in which P divides the line segment AB.

Mathematics - Board Papers