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JEE Main202331 Jan 2023Morning ShiftMathematicsThree Dimensional GeometryActual

Let the shortest distance between the lines L : x - 5 - 2 = y - λ 0 = z + λ 1 , λ ≥ 0 and L 1 : x + 1 = y - 1 = 4 - z be 2 6 . If ( α , β , γ ) lies on L , then which of the following is NOT possible?

Options

  1. Aα + 2 γ = 24
  2. B2 α + γ = 7
  3. C2 α - γ = 9
  4. Dα - 2 γ = 19

Correct answer

A. α + 2 γ = 24

Step-by-step solution

Given equations of lines are L :   x - 5 - 2 = y - λ 0 = z + λ 1 = k L 1 :   x + 1 1 = y - 1 1 = z - 4 - 1 Here, b 1 → × b 2 → = i ^ j ^ k ^ - 2 0 1 1 1 - 1 ⇒ b 1 → × b 2 → = - i ^ - j ^ - 2 k ^ And, a 2 → - a 1 → = 6 i ^ + λ - 1 j ^ + - λ - 4 k ^ ∵ Shortest distance is 2 6 . ⇒ 2 6 = - 6 - λ + 1 + 2 λ + 8 1 + 1 + 4 ⇒ | λ + 3 | = 12 ⇒ λ = 9 , - 15 ⇒ α = - 2 k + 5 ,   γ =

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