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Question
If a plane meets the co-ordinate axes at A, B, C such that the centroid of the triangle ABC is the point (u, v, w), find the equation of the plane
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Solution
Equation of the plane is `x/"A" + y/"B" + z/"C"` 1 ......(1)
By the defne of the centriced `("A"/3, "B"/3, "C"/3) = (u, v, w)`
A = `3u`
B = `3v`
C = `3w`
(1) ⇒ `x/(3u) + y/(3v) + z/(3w)` = 1
`1/3(x/u + y/v + z/w)` = 1
`x/u + y/v + z/w` = 3
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