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MHT CET202521 Apr 2025Evening ShiftMathematicsThree Dimensional GeometryActual

The direction ratios of the line of intersection of the planes x-y+z-5=0 and x-3 y-6=0 , are

Options

  1. A1,-1,1
  2. B1,-3,0
  3. C3,1,-2
  4. D1,2,0

Correct answer

C. 3,1,-2

Step-by-step solution

The planes are given by P₁: x - y + z - 5 = 0 and P₂: x - 3y - 6 = 0 . Their normal vectors are n₁ = (1, -1, 1) and n₂ = (1, -3, 0) respectively. The direction vector of the intersection line must be perpendicular to both normals, obtained from d = n₁ n₂ . d = (1, -1, 1) (1, -3, 0) = (3, 1, -2) Among the given options, the direction ratios (3, 1, -2) match option C. Answer: C

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