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JEE Main202226 Jun 2022Evening ShiftMathematicsThree Dimensional GeometryActual

If the lines r → = i ^ - j ^ + k ^ + λ 3 j ^ - k ^ and r → = α i ^ - j ^ + μ 2 i ^ - 3 k ^ are co-planar, the the distance of the plane containing these two lines from the point α , 0 , 0 is

Options

  1. A2 9
  2. B2 11
  3. C4 11
  4. D2

Correct answer

B. 2 11

Step-by-step solution

Given, r → = i ^ - j ^ + k ^ + λ 3 j ^ - k ^             . . . L 1 r → = α i ^ - j ^ + μ 2 i ^ - 3 k ^   L 1 and L 2 are coplanar then a 2 - a 1 b 1 b 2 = 0 So, 0 3 - 1 2 0 - 3 1 - α 0 1 = 0 - 3 2 + 3 1 - α = 0 3 α = 5 ⇒ α = 5 3 Now, normal vector will be, n → = i ^ j ^ k ^ 0 3 - 1 2 0 - 3 = i ^ - 9 - j ^ 2 + k - 6 = 9 , 2 , 6 So, equation of plane is given by, 9 x - 1 + 2 y + 1 + 6 z - 1 = 0 9 x + 2 y + 6 z - 13 = 0 Now f

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