Relative to the origin O, three distinct fixed points A, B and C have position vectors a, b and c respectively. It is known that b is a unit vector, |a|=3, |c| = 2 and the angle AOC is 60º.
(i) State the geometrical interpretation of |b⋅c|.
It is further given that .
(ii) Find the ratio of the area of triangle AOB to the area of triangle BOC.
(iii) Show that where 2a + c = k b where k∈ℜ, k≠0 ,.
By considering (2a + c)⋅(2a + c) , find the exact values of k.