If a plane meets the coordinates axes at A, Band C, in such a way that the centroid of `Delta ABC` is at the point `(1,2,3)`, the equation of the plane is

Options

A. `x/1+y/2+z/3=1`
B. `x/3+y/6+z/9=1`
C. `x/1+y/2+z/3=1/3`
D. none of these

Answer

B

Explanation

Let the equation of the required plane be `x/a+y/b+z/c=1`. This meets the coordinate axes at `A(a,0,0),B(0,b,0)` and `C(0,0,c)` the coordinates of the centroid of `Delta ABC` are `(a//3,b//3,c//3)`.
`:.a/3=1,b/3=2` and `c/3=3impliesa=3,b=6` and `z/9=1`.