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AP EAMCET202422 May 2024Morning ShiftMathematicsVector AlgebraActual

In P Q R,(4 i +3 j +6 k ),(2 i +2 j +3 k ) and (3 i + j +3 k ) are the position vectors of the vertices P , Q and R respectively. Then the position vector of the point of intersection of the angle bisector of P with QR is

Options

  1. A6 i +5 j +9 k
  2. B2 i - j +3 k
  3. C(5 i +3 j -2 k )
  4. D5 2 i + 3 2 j +3 k

Correct answer

D. 5 2 i + 3 2 j +3 k

Step-by-step solution

aligned & P R= 1+4+9 = 14 & P Q= 4+1+9 = 14 & P R=P Q aligned P Q R is isoceles triangle. Let A be the position vector of point of intersection of angle bisector of angle P and Q R . A is mid point of Q R . A (5 i +3 j +6 k ) 2 = 5 2 i + 3 2 j +3 k

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