If a plane meets the coordinate axes in A,B and C such that the centroid of `triangleABC`is (1,2,4), then the equation of the plane is

Options

A. `x+2y+4z=6`
B. 4x+2y+3z=12`
C. `x+2y+4z=7`
D. `4x+2y+z=7`

Answer

b

Explanation

Let the required equation of the plane be `x/a+y/b+z/c=1`.
Then, it meets the coordinate axes in `A(6,0,0), B(0,4,0)` and C(0,0,3).
`therefore` centroid of `triangleABC` is `G((a+0+0)/3,(0+b+0)/3,(0+0+c)/3)`, i.e., `G(a/3,b/3,c/3)`.
`therefore (a/3=1, b/3=2,c/3=4) rArr a=3,b=6,c=12`.