VITEEE 2014 Paper

Let the equation of the plane is

x

α

+

y

β

+

z

γ

= 1
Then, A (α, 0,0), B( 0, β, 0) and C(0,0, γ) are the points on the coordinate axes,
The centroid of the triangle is (1,2,4).
∴ α3 = 1 ⇒ α = 3

β

3

= 2 ⇒ β = 6
and

γ

3

= 4 ⇒ γ = 12
∴ The equation of the plane is

x

3

+

y

6

+

z

12

= 1
⇒ 4x + 2y + z = 12