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
D. a - b +3 c 3
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
Related: Mathematics — Vector Algebra · All PYQ Banks