OABC is a parallelogram. OA is represented by the vector a and OC is represented by the vector C.

M is the mid-point of BC and N is the point on OB such that
ON:NB = 2:1.

1. Find expressions for these vectors, giving the answers in the
simplest form: ON, OM, AN and AM.

2. Show that points A, N and M lie on a straight line.