A plane meets the coordinate axes in A,B,C such that the centroid of triangle ABC is the point `(p,q,r)`. If the equation of the plane is `x/p+y/q+z/r=k` then `k=`

Options

A. 3
B. 2
C. 1
D. 5

Answer

A

Explanation

Given, `(x)/(a)+(y)/(b)+(z)/(c)=krArr(x)/(ak)+(y)/(bk)+(z)/(ck)=1`
`:.` Coordinates of A,B and C are (ak,0,0), (0,bk,0) and (0,0,ck) respectively.
Also , given centroid of `DeltaABC` is
`((ak+0+0)/(3),(0+bk+0)/(3),(0+0+ck)/(3))`
`:." "a=(ak+0+0)/(3)rArrk=3`