The position vectors of points A and B relative to an origin O are a and b respectively. The point P is such that OP(vectors) = µOA(vectors). The point Q is such that OQ(vectors) = λOB(vectors). The lines AQ and BP intersects at the point R.

i. Express AQ(vectors) in terms of λ, a and b.

ii. Express BP(vectors) in terms of µ, a and b.

It is given that 3AR(vectors) = AQ(vectors) and 8BR(vectors) = 7BP(vectors).

iii. Express OR(vectors) in terms of λ, a and b.

iv. Express OR(vectors) in terms of µ, a and b.

v. Hence find the value of µ and of λ.

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R B