A plane which remains at a constant distance 3p from the origin cuts the co-ordinate axes at A, B and C. Show that the locus of the centroid of triangle ABC is x-2 +  y-2 + z-2 = p-2.

Asked by Topperlearning User | 4th Jun, 2014, 01:23: PM

Expert Answer:

Let a, b, c are the intercepts made by the plane with the co-ordinate axes, then the co-ordinates of A, B and C are (a, 0, 0), (0, b, 0) and (0, 0, c) respectively.

Then the equation of the plane is .                                          …(1)
Also, the perpendicular distance of this plane from the origin is 3p.
Now, let (x, y, z) be the co-ordinates of the centroid of the triangle ABC, then
On putting the values of a, b and c in (2), we get
 

Answered by  | 4th Jun, 2014, 03:23: PM