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 Form 3 Mathematics: Vectors II Questions and Answers

In triangle OPQ below, OP=p, OQ=q. Point M lies on OP such that OM:MP=2:3 and point N lies on OQ such that ON:NQ=5:1. Line PN intersects line MQ at X.
(a) Express in terms of p and q:
(i) PN
(ii) QM
(b) Given that PX=kPN and QX=rQM, where k and r are scalers:
(i) Write two different expressions for OX in terms of p, q, k and r.
(ii) Find the values of k and r.
(iii) Determine the ratio in which X divides line MQ.

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