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 2**a** + **c** = *k* **b** where *k*∈ℜ, *k*≠0 ,.

By considering (2**a** + **c**)**⋅**(2**a **+** c**) , find the exact values of *k*.

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