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AP EAMCET202119 Aug 2021Evening ShiftMathematicsThree Dimensional GeometryActual

Let L 1 (respectively L 2 ) be the line passing through 2 i ^ - k ^ (respectively 2 i ^ + j ^ - 3 k ^ ) and parallel to 3 i ^ - j ^ + 2 k ^ (respectively i ^ - 2 j ^ + k ^ ). Then the shortest distance between the lines L 1 and L 2 is equal to

Options

  1. A10 35
  2. B8 35
  3. C11 35
  4. D9 35

Correct answer

D. 9 35

Step-by-step solution

Given that line L 1 passes through 2 i ^ - k ^ and parallel to 3 i ^ - j ^ + 2 k ^ and line L 2 passes through 2 i ^ + j ^ - 3 k ^ and parallel to i ^ - 2 j ^ + k ^ . Then, a 1 = 2 i ^ - k ^ , b 1 = 3 i ^ - j ^ + 2 k ^ and a 2 = 2 i ^ + j ^ - 3 k ^ , b 2 = i ^ - 2 j ^ + k ^ Shortest distance between lines is given by, d = b → 1 × b → 2 · a → 2 - a → 1 b → 1 × b → 2 . Now, b → 1 × b → 2 = i ^ j ^ k ^ 3 - 1 2 1 - 2 1 = 3 i ^ - j ^ - 5 k ^ ⇒ b &

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