Vectors GCSE 9 1, iGCSE, A Level

In the diagram, O is the origin and points A and C have position vectors 𝒂 and 𝒄 𝒓𝒆𝒔𝒑𝒆𝒄𝒕𝒊𝒗𝒆𝒍𝒚.
D, M and C are points on OA, OC and AB respectively, such that OD: DA = 1 : 4, OM :MC = 3 : 2 and AC : CB = 5 :1