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99 Percentile Qs Bank for JEE MainMathematicsVector Algebra

The position vectors of the points A and B with respect to a fixed point O (origin) are 2 i ^ + 2 j ^ + k ^ and 2 i ^ + 4 j ^ + 4 k ^ . The length of the internal bisector of ∠ B O A of Δ A O B is

Options

  1. A1 3 6 9
  2. B1 3 6 3
  3. C2 0 3
  4. D2 1 7 9

Correct answer

B. 1 3 6 3

Step-by-step solution

OA → = 3 , OB → = 6 Position vector of L (internal bisector of ∠BOA) = OL → = OA → 2 i ^ + 4 j ^ + 4 k ^ + OB → 2 i ^ + 2 j ^ + k ^ OA → + OB → = 3 2 i ^ + 4 j ^ + 4 k ^ + 6 2 i ^ + 2 j ^ + k ^ 3 + 6 = 1 8 i ^ + 2 4 j ^ + 1 8 k ^ 9 = 1 3 6 i ^ + 8 j ^ + 6 k ^ So; OL → = 1 3 3 6 + 6 4 + 3 6 = 1 3 6 3 units

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