A plane meets the coordinate axes in `A ,B ,C` such that eh centroid of triangle `A B C` is the point `(p ,q ,r)dot` Show that the equation of the plane is `x/p+y/q+z/r=3.`

Explanation

Let the equation of the required plane be
` (x)/(a) + (y)/(b) + (z)/(c ) =1`
Then the coordinates of A, B, C are `(a, 0, 0), (0, b, 0), (0, 0, c)` respectively.
`therefore` the centroid of the triangle ABC is
`((a+0+0)/(3),(0+b+0)/(3),(0+0+c)/(3))i.e., ((a)/(3), (b)/(3),(c)/(3))`
BUt the coordinates of the centroid are `(p, q, r)`
`therefore (a)/(3)=p,(b)/(3)=qand(c)/(3)=r`
`therefore a =3p,b=3qandc=3r`
`therefore` from (1), the equation of the required plane is
`(x)/(3p) + (y)/(3q) + (z)/(3r) =1`
i.e., `(x)/(p) + (y)/(q) + (z )/(r ) =3.`