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AP EAMCET202022 Sep 2020Morning ShiftMathematicsThree Dimensional GeometryActual

Equation of the plane passing through the intersection of the lines x-1 1 = y-2 2 = z-5 -3 and x+5 3 = y-4 -1 = z+3 4 and parallel to the x y -plane is

Options

  1. Az=4
  2. Bz=2
  3. Cz=5
  4. Dz=-5

Correct answer

C. z=5

Step-by-step solution

Equation of given lines x-1 1 = y-2 2 = z-5 -3 =r₁ (Iet) and x+5 3 = y-4 -1 = z+3 4 =r₂ (let) are intersecting lines, then on equating the parametric points on lines, we get aligned r₁+1 & =3 r₂-5 2 r₁+2 & =-r₂+4 and -3 r₁+5 & =4 r₂+3 aligned So on solving, r₁=0 and r₂=2 Point of intersection is A(1,2,5) . Now the equation of plane parallel to x y -plane and passes through point A is z=5 . Hence, option (3) is correct.

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