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MHT CET202615 April 2026Morning ShiftMathematicsThree Dimensional GeometryActual

If the lines x-5 5m+2 = 2-y 5 = 1-z -1 and x = 2y+1 4m = 1-z -3 are perpendicular to each other, then the value of m is ...

Options

  1. A1
  2. B0
  3. C2
  4. D-1

Correct answer

A. 1

Step-by-step solution

Rewriting the equations of the given lines in standard form. First line: x-5 5m+2 = y-2 -5 = z-1 1 Direction ratios of the first line are a₁ = 5m+2 , b₁ = -5 , c₁ = 1 . Second line: x-0 1 = y+ 1 2 2m = z-1 3 Direction ratios of the second line are a₂ = 1 , b₂ = 2m , c₂ = 3 . Since the lines are perpendicular, a₁ a₂ + b₁ b₂ + c₁ c₂ = 0 . (5m+2)(1) + (-5)(2m) + (1)(3) = 0 5m + 2 - 10m + 3 = 0 -5m + 5 = 0 m = 1 Answer: 1

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