A plane meets the coordinate axes at A, B and C such that the centroid of triangle ABC is (p, q, r). Then the equation of the plane is:
Correct: A
Let the coordinates of A, B, C be (a, 0, 0), (0, b, 0), and (0, 0, c) respectively. Then the equation of the plane is x/a + y/b + z/c = 1. The centroid of triangle ABC is ((a+0+0)/3, (0+b+0)/3, (0+0+c)/3) = (a/3, b/3, c/3). Given that the centroid is (p, q, r), we have p = a/3, q = b/3, and r = c/3. Thus, a = 3p, b = 3q, and c = 3r. Substituting these values in the equation of the plane, we get x/(3p) + y/(3q) + z/(3r) = 1 => x/p + y/q + z/r = 3.