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MHT CET202123 Sep 2021Evening ShiftMathematicsVector AlgebraActual

If 3 j , 4 k and 3 j +4 k are the position vectors of the vertices A , B , C respectively of ABC , then the position vector of the point in which the bisector of A meets BC is

Options

  1. A5 3 j -4 k
  2. B5 j -4 k
  3. C5 j +4 k
  4. D5 3 j +4 k

Correct answer

D. 5 3 j +4 k

Step-by-step solution

We have a =3 j , b =4 k and c =3 j +4 k Angle bisector AD divides BC in the ratio AB : AC AB = 9+16 =5 and AC = 0+16 =4 Thus D divides BC in the ratio 5: 4 aligned & D = [0, 5(3) 5+4 , 5(4)+4(4) 5+4 ] & = (0, 15 9 , 20+16 9 )= (0, 5 3 , 4 )= 5 3 j +4 k aligned

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