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 `A-=(a,0,0),B-=(0,b,0),C-=(0,0,c)`.
`:.` Equation of the plane in Intercept form is
`(x)/(a)+(y)/(b)+(z)/(c)=1" "......(i)`
`:'` (p,q,r) is the centroid of `DeltaABC`, we get
`p=(a+0+0)/(3),q=(0+b+0)/(3)`
`r=(0+0+c)/(3)`
`:.p=(a)/(3),q=(b)/(3),r=(c)/(3)`
`:.a=3p,b=3q,=3r`
Substituting in equation (i), we get
`(x)/(3p)+(y)/(3q)+(z)/(3r)=1`
`:.(1)/(3)((x)/(p)+(y)/(q)+(z)/(r))=1`
`:.(x)/(p)+(y)/(q)+(z)/(r)=3`.
This is the equation of plane.