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NTA Abhyas JEE Main2020MathematicsThree Dimensional GeometryPractice

The complete set of values of α for which the lines x - 1 2 = y - 2 3 = z - 3 4 and x - 3 2 = y - 5 α = z - 7 α + 2 are coplanar is

Options

  1. A2 , 3
  2. B0 , 3
  3. C- 2 , 3
  4. DR

Correct answer

D. R

Step-by-step solution

Any point on the first line is 1 + 2 λ , 2 + 3 λ , 3 + 4 λ , Any point on the second line is 3 + 2 μ , 5 + α μ , 7 + 2 μ + α μ Now, as they are intersecting 1 + 2 λ = 3 + 2 μ and 2 + 3 λ = 5 + α μ So, λ = μ + 1, hence 2 + 3 μ + 1 = 5 + α μ ⇒ α - 3 μ = 0 Hence for λ = 1 , μ = 0, the point 3 , 5 , 7 lies on both the lines irrespective of α . Hence, ∀ α ∈ R lines are concurrent

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