Question

A plane meets axis in A, B and C such that centroid of ? ABC is (1, 2, 3) then equation of plane is :

(a) x/1 + y/2 + z/3 = 1

(b) x/1 + y/2 + z/3 = 1/6

(c) (x - 1)/1 + (y - 2)/2 + (z - 3)/3 = 1

(d) x/3 + y/6 + z/9 = 1

Answer 1

Answer is (d)

Let equation of plane x/a + y/b + z/c = 1 

which meets the coordinate axis on points A (a,0,0), B(0,b,0) and C (0,0,c), then centroid of ∆ABC will be (a/3, b/3, c/3)

a/3 = 1, b/3 = 2, c/3 = 3

a = 3, b = 6, c = 9

Hence required equation of plane is x/3 + y/6 + z/9 = 1.