In rectangle ABCD, it is known that AD = a, DC = b, O is the intersection point of the diagonals. Find the value

In rectangle ABCD, it is known that AD = a, DC = b, O is the intersection point of the diagonals. Find the value: vector AO – vector BC + vector OD – vector OB + vector DC

Let the vectors AD = a; DC = b, we calculate the sum of vectors: AO + OD + CD – OB – BC = (AO + OD + DC) – (OB + BC). When calculating (summing vectors), we apply the rule. A new vector is added to the vector, and the end of the first vector serves as the beginning of the second vector. This is necessary then so as not to use the movement of vectors.
(AO + OD + DC) here the rule turns out that the end of the first vector coincides with the beginning of the second, and so on, then: AO + OD + DC = AC.
OB + BC = OС; -OС = CO, then AC + CO = AO = 1/2 AC = 1/2 (a + b).