A plane meets the coordinate axes at A, B and C such that the centroid of ∆ABC is the point (a, b, c). If the equation of the plane is x/a + y/b + z/c = k, then k =

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3 \text{ Let } \alpha, \beta \text{ and } \gamma \text{ be the intercepts of the given plane on the coordinate axes } . \text{ Then, the plane meets the coordinate axes at } A \left( \alpha, 0, 0 \right), B \left( 0, \beta, 0 \right) \text{ and } C = \left( 0, 0, \gamma \right) \text{ Given that the centroid of the triangle } =\left( a, b, c \right) \Rightarrow\left( \alpha + 0 + $\frac{0}{3}$, 0 + \beta + $\frac{0}{3}$, 0 + 0 + \gamma/3 \right)=\left( a, b, c \right) \Rightarrow\left( \alpha/3, \beta/3, \gamma/3 \right)=\left( a, b, c \right) \Rightarrow\alpha/3=a,\beta/3=b,\gamma/3=c \Rightarrow \alpha = 3a, \beta = 3b, \gamma = 3c . . . \left( 1 \right) \text{ Equation of the plane whose intercepts on the coordinate axes are } \alpha,\beta\text{ and} \gamma \text{ is} x/\alpha + y/\beta + z/\gamma = 1 \Rightarrow x/3a + y/3b + z/3c = 1.................... [\text{ From } (1)] \Rightarrow x/a + y/b + z/c = 3

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