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In the figure below, AB=p, AD=q, DE= `1/2`AB and BC= `2/3`BD.

(a) Find in terms of p and q, the vectors:
(i) BD
(ii) BC
(iii) CD
(iv) AC
(b) Given that AC=kCE, where k is a scaler, find:
(i) The value of k.
(ii) The ratio in which C divides AE.