Problem

(i) Relative to a fixed origin $O$, the points $A$, $B$ and $C$ have position vectors $a$, $b$ and $c$ respectively.

Points $A$, $B$ and $C$ lie in a straight line, with $B$ lying between $A$ and $C$.

Given that $AB:AC=1:3$ show that

$$c=3b-2a$$

(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