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Math Help - Equation for Projection of vector b onto vector a

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    Equation for Projection of vector b onto vector a

    Edited
    Let \theta be the angle between vectors \vec{a} and \vec{b}.

    We find the projection of \vec{b} onto \vec{a} by first drawing an altitude (perpendicular to \vec{a}) from the head of \vec{b} to \vec{a}. We have a right triangle, and by good old SOH CAH TOA, proj_{\vec{a}}\vec{b} = \left| \vec{b} \right|\cos(\theta), because \vec{b} is the hypotenuse.

    We also have that \cos(\theta) = \frac{\vec{a} \cdot \vec{b}}{\left|\vec{a}\right| \left|\vec{b}\right|}.

    When I substitute that into the equation for the projection of proj_{\vec{a}}\vec{b}, I get
    proj_{\vec{a}}\vec{b} = \left| \vec{b} \right| \cos(\theta) =\frac{\vec{a} \cdot \vec{b}}{\left|\vec{a}\right|}

    right?

    But that yields a number, not a vector.
    What am I (still) doing wrong?
    Last edited by MSUMathStdnt; April 6th 2013 at 05:46 PM.
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