Question
A plane meets the co-ordinate axes at A, B, C such that the centroid of the triangle ABC is the point (1, – 2, 3). Show that the equation of the plane is 6x-3y + 2z= 18.
Solution
Let the equation of plane be 
...(1)
It meets the 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.
∵ (1, – 2, 3) is centroid of triangle ABC
Putting values of a, b, c in (1), we get,
or 6 x – 3 y + 2 z = 18, which is required equation.
...(1)It meets the 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.
∵ (1, – 2, 3) is centroid of triangle ABC
Putting values of a, b, c in (1), we get,
or 6 x – 3 y + 2 z = 18, which is required equation.
