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JEE MainMathematicsThree Dimensional Geometry

Consider the lines L₁ and L₂ given by L₁ : x - 3 2 = y - 1 -1 = z - 9 1 L₂ : x - 1 1 = y 1 = z + 2 -2 A line L having direction ratios 1, 2, 3 intersects L₁ and L₂ at the points P and Q respectively. If the line L intersects the z-axis at the point (0, 0, ) , then the value of is

Options

  1. A3
  2. B7
  3. C10
  4. D5

Correct answer

D. 5

Step-by-step solution

Let the points on L₁ and L₂ be P and Q respectively. P = (2 + 3, - + 1, + 9) Q = ( + 1, , -2 - 2) The direction ratios of the line PQ are proportional to 1, 2, 3 . 2 - + 2 1 = - - + 1 2 = + 2 + 11 3 Taking the first two parts: 2(2 - + 2) = - - + 1 5 - + 3 = 0 = 5 + 3 Taking the first and third parts: 3(2 - + 2) = + 2 + 11 5 - 5 - 5 = 0 = - 1 Equating the values of : 5 + 3 = - 1 4 = -4 = -1 Then = -2 . Substituting = -1 into P , we get P(1, 2, 8) . The equation of the line L passing through P with direction ratios 1

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