IF VECTOR a AND VECTOR b ARE THE TWO VECTORS DETERMINED BY TWO ADJACENT SIDES OF A REGULAR HEXAGON.
Let's identify all the vectors in counterclockwise direction CD, DE, EF.
Also BC = b and it's anti parallel to EF.
Hence EF = -b. and FE = b
Similarly, DE = -a.
Similarly AF = CD
AC = AB + BC = a + b
AD = AC + CD = a + b + AF
AE = AD + DE = a + b + AF - a = b + AF