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In the figure below, ABCD is a parallelogram in which BC is produced to X such that BC=CX. Y is the mid-point of DC and AYX is a straight line.
(a) Given that AB=a and BC=b, express the following vectors in terms of a and b.
(i) CX
(ii) AC
(iii) AX
(iv) DX
(b) Use vectors to prove that ACXD is a parallelogram.