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JEE Main2014MathematicsThree Dimensional GeometryActual

Equation of the plane which passes through the point of intersection of lines x - 1 3 = y - 2 1 = z - 3 2 and x - 3 1 = y - 1 2 = z - 2 3 and has the largest distance from the origin is:

Options

  1. A4 x + 3 y + 5 z = 50
  2. B3 x + 4 y + 5 z = 49
  3. C5 x + 4 y + 3 z = 57
  4. D7 x + 2 y + 4 z = 54

Correct answer

A. 4 x + 3 y + 5 z = 50

Step-by-step solution

Line L 1 : x - 1 3 = y - 2 1 = z - 3 2 = λ L 2 : x - 3 1 = y - 1 2 = z - 2 3 = μ ⇒    x = 3 λ + 1 and x = μ + 3        y = λ + 2   y = 2 μ + 1         z = 2 λ + 3   z = 3 μ + 2 ⇒ 3 λ + 1 = μ + 3 ⇒ 3 λ - μ = 2 λ + 2 = 2 μ + 1 ⇒ λ - 2 μ = - 1 2 λ + 3 = 3 μ + 2 ⇒ 2 λ - 3 μ = - 1 Solving μ = 1 ,   &#955

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