1. Relative to an origin $O$, the points $A,B$ and $C$ have position vectors $p,3q-pand9q-5p$ respectively.

(i) Find $\overset{\rightarrow}{AB}$ in terms of $p$ and $q$.

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(ii) Find $\overset{\rightarrow}{AC}$ in terms of $p$ and $q$.

[1]

(iii) Explain why $A,BandC$ all lie in a straight line.

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(iv) Find the ratio $AB:BC$.

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