Your solution is wrong ... BC vector =a ... then AD vector =CD vector -AC vector ... CD vector is opposite to (1/2)a vector ... so AD=CD-AC=-( 1/2)a-b ... and then AD+Be+. -(1/2) a-b+a+(1/2) b+cf = 0 ... and then get (3). The value of vector AD is wrong (the vector symbol is difficult to type, so the vector symbol is omitted below).

AD=AC+CD=-b- 1/2*a