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Find the equation of the plane that cuts the coordinate axes so as to form a triangle whose centroid is at (α, β, γ).

1. αx + βy + γz = 3
2. αx + βy + γz = 1
3. x/α + y/β + z/γ = 3
4. x/α + y/β + z/γ = 1

Correct answer: x/α + y/β + z/γ = 3

Solution

The correct option represents a plane that intersects the coordinate axes at points proportional to α, β, and γ, forming a triangle with a centroid at (α, β, γ). The equation x/α + y/β + z/γ = 3 indicates that the intercepts are scaled such that the centroid aligns with the specified coordinates.

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