Question
A plane meets the coordinate axes in A, B, C and (α, β, γ) is the centroid of the triangle ABC. Then, show that the equation of the plane is 
Solution
Let the equation of plane be
...(1)
It meets x = axis in A where y = 0, z = 0
Putting y = 0, z = 0 in (1), we get,
∴ A is (a, 0, 0)
Similarly B, C are (0, b, 0), (0, 0, c) respectively.
∵ (α, β,γ) is centroid of ΔABC
Putting values of a, b, c in (1), we get,
or
which is required equation of plane.
...(1)It meets x = axis in A where y = 0, z = 0
Putting y = 0, z = 0 in (1), we get,
∴ A is (a, 0, 0)
Similarly B, C are (0, b, 0), (0, 0, c) respectively.
∵ (α, β,γ) is centroid of ΔABC
Putting values of a, b, c in (1), we get,
or
which is required equation of plane.
