The eqution of the plane which meets the axes in A,B,C such that the centroid of the `Delta BAC is ((1)/(3)(1)/(3),(1)/(3))` is given by

Options

A. `x+y+z=1`
B. `x+y+z=2`
C. `(x)/(3)+(y)/(3)+(z)/(3)=3`
D. `x+y+z=(1)/(3)`

Answer

A

Explanation

Let thye equation of plane be
`(x)/(a)+(y)/(b)+(z)/(c)=1" "...(i)`
Then, coordinates of A,B, and C are `(a,0,0),(,0,b,0) and (0,0,c)` resepectively.
The centroid of a `Delta ABC is ((a)/(3),(b)/(3),(c)/(3))`
but is given `((1)/(3),(1)/(3),(1)/(3))`.
`:. (a)/(3)=(1)/(3),(b)/(3) =(1)/(3),(c)/(3)=(1)/(3)`
`rArr a=b=c=1`
`:.` From Eq. (i) `x+y+z=1`