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JEE Main201815 Apr 2018Evening ShiftMathematicsVector AlgebraActual

If the position vectors of the vertices A, B and C of a ABC are respectively 4 i +7 j +8 k , 2 i +3 j +4 k and 2 i +5 j +7 k , then the position vector of the point, where the bisector of A meets B C is

Options

  1. A1 2 (4 i +8 j +11 k )
  2. B1 3 (6 i +13 j +18 k )
  3. C1 4 (8 i +14 j +9 k )
  4. D1 3 (6 i +11 j +15 k )

Correct answer

B. 1 3 (6 i +13 j +18 k )

Step-by-step solution

Suppose angular bisector of A meets B C at D (x, y, z) Using angular bisector theorem, aligned A B A C &= B D D C B D D C &= (4-2)^2+(7-3)^2+(8-4)^2 (4-2)^2+(7-5)^2+(8-7)^2 &= 2^2+4^2+4^2 2^2+2^2+1^2 = 6 3 =2 aligned D(x, y, z)= ( 6 3 , 13 3 , 18 3 ) Therefore, position vector of point P= 1 3 (6 i+13 j+18 k)

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