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MHT CET2019Evening ShiftMathematicsThree Dimensional GeometryActual

If line x - 1 2 = y + 1 3 = z - 1 4 and x - 3 1 = y - λ 2 = z 1 intersect each other, then λ = . … .

Options

  1. A7 2
  2. B3 2
  3. C9 2
  4. D5 2

Correct answer

C. 9 2

Step-by-step solution

Given lines are x - 1 2 = y + 1 3 = z - 1 4 = λ 1 l e t ….. (i) a n d x - 3 1 = y - λ 2 = z 1 = λ 2 l e t …… (ii) is Then, any point on line (i) is 2 λ 1 + 1,3 λ 1 - 1,4 λ 1 + 1 and any point on line (ii) is λ 2 + 3,2 λ 2 + λ , λ 2 Clearly, then lines (i) and (ii) will intersect if 2 λ 1 + 1,3 λ 1 - 1,4 λ 1 + 1 = λ 2 + 3,2 λ 2 + λ , λ 2 For some particular value of λ 1 and λ 2 ⇒ 2 λ 1 + 1 = λ 2 + 3,3 λ 1 - 1 = 2 λ 2 + λ a n d 4 λ 1 + 1 = λ 2 ⇒ 2 λ 1 - λ 2 , 3 λ 1 - 2 λ 2 = λ + 1 and 4 λ 1 - λ 2 = - 1 We

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