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+y//2+z//3=1`
B. `x//3+y//6+z//9=1`
C. `x+2y+3z=1`
D. None of the above

Answer

B

Explanation

Let the plane meets the coordinate axes at A, B and C.
Let `OA=a, OB=b and OC=c`

Then, the centroid of `DeltaABC`
is `((a)/(3),(b)/(3),(c)/(3))=(1,2,3)` (given)
`impliesa=3, b=6, c=9`
Then, the equation of plne meet the coordinate axes is
`x/a+y/b+z/c=1`
i.e., `x/3+y/6+z/9=1`