The parallelogram OABC has it vertices at O (origin) and points A, B and C with poisition vectorsa,bandcrespectively. The point P is the mid point of AB and the point Q is the midpoint of BC. The line CP meets the line OQ at the point R ( intersection of lines)

a) write down in terms ofaandc, the position vectorsb,pandqof the points B, P and Q respectively.

b) Show that every point on the line CP has a position vector x of the form;

x=(1-k)a+ 1/2(1-k)cwhere k is any real number

c) Find thevalue of k in the above formula such that x is a scalar multiple ofq