Correct Answer - A
Given plane cuts the coordinate axes at `A(a,0,0),B(0,b,0)` and `C(0,0,0)`. It is at a unit distance from the origin.
`:.1/(sqrt(1/(a^(2))+1/(b^(2))+1/(c^(2))))=1implies1/(a^(2))+1/(b^(2))+1/(c^(2))=1`……………i
Since `(x,y,z)` is the centroid of `DeltaABC`.
`:.x=a/3,y=b/3,z=c/3impliesa=3x,b=3y,c=3z`
Substituting the values of `a,b,c` in (i) we get
`1/(x^(2))+1/(y^(2))+1/(z^(2))=9impliesk=9`