(i) Relative to a fixed origin $$\(O\)$$, the points $$\(A, B\)$$ and $$\(C\)$$ have position vectors $$\(\mathbf{a}, \mathbf{b}\)$$ and $$\(\mathbf{c}\)$$ respectively. Points $$\(A, B\)$$ and $$\(C\)$$ lie in a straight line, with $$\(B\)$$ lying between $$\(A\)$$ and $$\(C\)$$. Given $$\(A B: A C=1: 3\)$$ show that $$\[ \mathbf{c}=3 \mathbf{b}-2 \mathbf{a} \]$$ (3) (ii) Given that $$\(n \in \mathbb{N}\)$$, prove by contradiction that if $$\(n^{2}\)$$ is a multiple of 3 then $$\(n\)$$ is a multiple of 3 (5)

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