9. (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 $$\mathbf { c } = 3 \mathbf { b } - 2 \mathbf { a }$$ (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