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A line parallel to 6 i ^ - 3 j ^ + 2 k ^ intersects the line x 1 = y 2 = z 2 at A and the line x + 1 1 = y + 2 2 = z + 3 2 at B , then the length of A B is equal to

Options

  1. A3 7 units
  2. B5 439 units
  3. C7 85 units
  4. D9 425 units

Correct answer

C. 7 85 units

Step-by-step solution

Both the given lines are parallel to b → = i ^ + 2 j ^ + 2 k ^ Let the angle between the line and 6 i ^ - 3 j ^ + 2 k ^ is θ ∴ cos θ = i ^ + 2 j ^ + 2 k ^ ⋅ 6 i ^ − 3 j ^ + 2 k ^ 3 × 7 = 4 21 Let the 1 s t line is passing through a → = 0 → and the 2 n d line is passing through c → = - i ^ - 2 j ^ - 3 k ^ A C = distance between the parallel lines = a → - c → × b → b → = i ^ + 2 j ^ + 3 k ^ × i ^ + 2 j ^ + 2 k ^ 3 = 5 3 ∴ A B = A C sec ⁡ 90 - θ = A C cosec θ = 5 3 × 21 425 = 7 85

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