# Math Help - Vector Question

1. ## Vector Question

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

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

2. $\vec{p}_{||}=\left(\dfrac{\vec{a}\cdot\vec{b}}{\ve c{a}\cdot\vec{a}}\right)\vec{a}$ and $\vec{p}_{\bot}=\vec{p}-\vec{p}_{||}$