Question

A variable plane at a distance of 1 unit from the origin cuts the co-ordinate axes at a,b,c. If the centroid d(x,y,z) of triangle abc

Answer 1

let the plane be x/a + y/b + z/c = 1  with x,y,z intercepts as a, b, c respectively.

given perpendicular distance is 1, so

1/a2 +1/b2 + 1/c2 = 1

centroid is (a/3, b/3, c/3)

so 9/a2 +9/b2 +9/c2 = k   which implies

k=9