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Math Help - Vector Question

  1. #1
    Junior Member CuriosityCabinet's Avatar
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    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.
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  2. #2
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    \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}_{||}
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