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JEE MainMathematicsThree Dimensional Geometry

Let a line L intersect the lines x-1 = y-2 = a-z and x-3 = 4-y = z-4 , and be parallel to the line x=y=z . If the distance between the points of intersection is 2 3 and a > 5 , then the value of a is

Options

  1. A2
  2. B8
  3. C10
  4. D12

Correct answer

C. 10

Step-by-step solution

Let the given lines be L₁ and L₂ . L₁: x-1 1 = y-2 1 = z-a -1 = L₂: x-3 1 = y-4 -1 = z-4 1 = A general point on L₁ is A( +1, +2, - +a) and on L₂ is B( +3, - +4, +4) . The direction ratios of the line segment AB are - + 2, - - + 2, + + 4 - a . Since L is parallel to the line x=y=z , the direction ratios of AB are proportional to 1, 1, 1 . Let - + 2 = k , - - + 2 = k , and + + 4 - a = k . From the first two equations: - + 2 = - - + 2 2 = 0 = 0 Substituting = 0 into the first equation gives = 2 - k . Substituting = 0

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