Question

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=`
A. 1
B. 2
C. 3
D. none of these

Answer 1

Correct Answer - C
Let the equation of the required plane be
`x/a+y/b+z/c=1`…………….i
Then the coordinates of A,B and C are `A(a,0,0),B(0,b,0)` and `C(0,0,c)` are respectively.
So, the centroid of triangle ABC is `(a//3,b//3,c//3)`
But the coordinates of the centroid are `(p,q,r)`
`:.p=a/3,q=b/3` and `r=c/3impliesa=3p,b=3q` and `c=3r`
Substituting the values of a,b and c in i , we obtain the required plane as
`x/(3p)+y/(3q)+z/(3r)=1impliesx/p+y/q+z/r=3`