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MHT CET202620 April 2026Morning ShiftMathematicsThree Dimensional GeometryActual

A plane meets the co-ordinate axes in A, B, C such that the centroid of the triangle ABC is the point (1, r, r^2) , then the equation of the plane is,

Options

  1. Ax + ry + r^2 z = 3r^2
  2. Br^2 x + ry + z = 3r^2
  3. Cx + ry + r^2 z = 3
  4. Dr^2 x + ry + z = 3

Correct answer

B. r^2 x + ry + z = 3r^2

Step-by-step solution

Let the coordinates of the points where the plane meets the axes be A(a, 0, 0) , B(0, b, 0) , and C(0, 0, c) . The equation of the plane in intercept form is x a + y b + z c = 1 . The centroid of the triangle ABC is given by ( a 3 , b 3 , c 3 ) . Given that the centroid is (1, r, r^2) , we have: a 3 = 1 a = 3 b 3 = r b = 3r c 3 = r^2 c = 3r^2 Substituting the values of a , b , and c into the equation of the plane, we get: x 3 + y 3r + z 3r^2 = 1 Multiplying the entire equation by 3r^2 , we obtain: r^2 x + ry + z =

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