A plane intersects the coordinate axes in A, B and C, respectively. If

1.	A plane intersects the coordinate axes in A, B and C, respectively. If (α,β,γ) is the centroid of Δ ABC, then show that the equation of the plane x/α + y/β + z/γ = 3
Answer» Let A = (a,0,0), B = (0,b,0) and C = (0,0,c) so that G = (a/3, b/3, c/3) and the equation of the plane is x/a + y/b + z/c = 1 ...(1) Since (α, β, γ) is the centroid, we have α = a/3, β = b/3, γ = c/3 a = 3α, b = 3β, c = 3γ so that from Eq. (1), the equation of the planes is x/α + y/β + z/γ = 3

A plane intersects the coordinate axes in A, B and C, respectively. If (α,β,γ) is the centroid of Δ ABC, then show that the equation of the plane x/α + y/β + z/γ = 3

Answer»

Let A = (a,0,0), B = (0,b,0) and C = (0,0,c) so that

G = (a/3, b/3, c/3)

and the equation of the plane is

x/a + y/b + z/c = 1 ...(1)

Since (α, β, γ) is the centroid, we have

α = a/3, β = b/3, γ = c/3

a = 3α, b = 3β, c = 3γ

so that from Eq. (1), the equation of the planes is

x/α + y/β + z/γ = 3

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A plane intersects the coordinate axes in A, B and C, respectively. If (α,β,γ) is the centroid of Δ ABC, then show that the equation of the plane x/α + y/β + z/γ = 3

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