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AP EAMCET202120 Aug 2021Morning ShiftMathematicsThree Dimensional GeometryActual

The position vectors of the points A and B with respect to O are 2 i ^ + 2 j ^ + k ^ and 2 i ^ + 4 j ^ + 4 k ^ . The length of the internal bisector of ∠ B O A of ∆ A O B is (take proportionality constant is 2 )

Options

  1. A136 9
  2. B136 3
  3. C20 3
  4. D25 3

Correct answer

B. 136 3

Step-by-step solution

Here  OA = 2 2 + 2 2 + 1 2 = 3 ,   OB = 2 2 + 4 2 + 4 2 = 6 So, Internal bisector  O D  divides  A B  in the ratio   = 1 : 2 , using angle bisector theorem Using section formula, we get Position vectors of  D  are   ( 2 ,   8 ​ 3 , 2 ) ∴ O D =     4 +   64   9 + 4   ​ = 136 3

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