The figure shows points A, B and C with position vectors a, b and c respectively, relative to an origin O. The point P lies on AB such that AP: AB = 3: 4. The point Q lies on OC such that OQ:QC = 2: 3.

i. Express AP(vectors) in terms of a and b and hence show that OP(vectors) = ¼(a + 3b).

ii. Find PQ(vectors) in terms of a, b and c.

iii. Given that 5 PQ(vectors) = 6BC(vectors), find c in terms of a and b.