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NDA2017MathematicsThree Dimensional GeometryActual

Under which one of the following conditions are the lines x = ay + b ; z = cy + d and x = ey +f ; z = gy + h perpendicular?

Options

  1. Aae + cg -1=0
  2. Bae + b f-1=0
  3. Cae + cg +1=0
  4. Dag + ce +1=0

Correct answer

C. ae + cg +1=0

Step-by-step solution

Given, lines x = ay + b and z = cy + d are perpendicular. x-b a = y 1 = z-d c ...(i) Also, x=e y+f and z=g y+h are perpendicular. x - f e = y 1 = z - h ~g ...(ii) We know, for ^r lines a₁ a₂+b₁ b₂+c₁ c₂=0 ae +1+ cg =0

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