Question
A variable plane is at a constant distance p from the origin and meets the axes in A, B and C respectively, then show that locus of the centroid of the triangle ABC is
Solution
Let O be the origin and OA = a, OB.= b, OC = c.
∴ the equation of plane passing through A, B and C is
or 
From the given condition,
Now A, B, C are (a, 0,0), (0, b, 0), (0, 0, c) respectively.
Let (x1 ,y1 , z1) be the centroid of ΔABC.
Putting values of a, b, c in (1), we get,
or 
∴ locus of centroid (x1 ,y1, z1) is
