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BITSAT2024MathematicsVector AlgebraActual

Let ABC be a triangle and be a , b , c the position vectors of A , B , C respectively. Let D divide B C in the ratio 3: 1 internally and E divide AD in the ratio 4: 1 internally. Let BE meet AC in F . IfE divides BF in the ratio 3: 2 internally then the position vector of F is

Options

  1. Aa + b + c 3
  2. Ba -2 b +3 c 2
  3. Ca +2 b +3 c 2
  4. Da - b +3 c 3

Correct answer

D. a - b +3 c 3

Step-by-step solution

Here we are given that OA = a , OB = b , OC = c Now P.V of Di.e OD = 1 OB +3 OC 1+3 aligned & OD = b +3 c 4 & OE = 4 OD + OA 4+1 = 4( ~b +3 c ) 4 + a 5 & OE = a + b +3 c 5 & Now, OE = 2 OB +3 OF 2+3 & OF = 5 OE -2 OB 3 & OF = 5( a + b +3 c ) 5 -2 ~b 3 & OF = a - b +3 c 3 P . V . of F is a - b +3 c 3 aligned

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