The vectors $\displaystyle \mathbf{a}$ and $\displaystyle \mathbf{b}$ lie in the plane $\displaystyle \Pi$. Given that $\displaystyle \left | a \right | = 1$ and a$\displaystyle \cdot b = 3$, find, in terms of $\displaystyle \mathbf{a}$ and $\displaystyle \mathbf{b}$, a vector $\displaystyle \mathbf{p}$ parallel to $\displaystyle \mathbf{a}$ and a vector $\displaystyle \mathbf{q}$ perpendicular to $\displaystyle \mathbf{a}$, both lying in the plane $\displaystyle \Pi$, such that

$\displaystyle \mathbf{p}+\mathbf{q} = \mathbf{a}+\mathbf{b}$.

Can anyone give me clues as to how to get started with this question? Thanks in advance.