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Question

A plane meets the coordinate axes at A, B and C, respectively, such that the centroid of triangle ABC is (1, −2, 3). Find the equation of the plane.

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Solution

Let a, b and c be the intercepts of the given plane on the coordinate axes.Then the plane meets the coordinate axes atA a, 0, 0, B 0, b, 0 and C 0, 0, cGiven that the centroid of the triangle is 1, -2, 3a+0+03, 0+b+03, 0+0+c3 = 1, -2, 3a3, b3, c3 = 1, -2, 3a3 = 1, b3 = -2, c3 = 3a = 3, b =-6, c = 9 ... 1Equation of the plane whose intercepts on the coordinate axes are a, b and c isxa + yb + zc = 1x3 + y-6 + z9 = 1 [From (1)]6x - 3y + 2x = 18

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