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Math Help - Find all vector

  1. #1
    Super Member dhiab's Avatar
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    Find all vector

    Find all vector
    {\mathord{\buildrel{\lower3pt\hbox{$\scriptscripts  tyle\rightharpoonup$}} <br />
\over v} }<br />


    such that :

    \mathord{\buildrel{\lower3pt\hbox{$\scriptscriptst  yle\rightharpoonup$}} <br />
\over v} .\mathord{\buildrel{\lower3pt\hbox{$\scriptscripts  tyle\rightharpoonup$}} <br />
\over v} + 2\mathord{\buildrel{\lower3pt\hbox{$\scriptscripts  tyle\rightharpoonup$}} <br />
\over u} .\mathord{\buildrel{\lower3pt\hbox{$\scriptscripts  tyle\rightharpoonup$}} <br />
\over v} = \alpha
    and :
    <br />
\begin{array}{l}<br />
\alpha :const - value \\ <br />
\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptst  yle\rightharpoonup$}} <br />
\over u} :const - vector \\ <br />
\end{array}
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  2. #2
    MHF Contributor
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    Quote Originally Posted by dhiab View Post
    Find all vector
    {\mathord{\buildrel{\lower3pt\hbox{$\scriptscripts  tyle\rightharpoonup$}} <br />
\over v} }<br />


    such that :

    \mathord{\buildrel{\lower3pt\hbox{$\scriptscriptst  yle\rightharpoonup$}} <br />
\over v} .\mathord{\buildrel{\lower3pt\hbox{$\scriptscripts  tyle\rightharpoonup$}} <br />
\over v} + 2\mathord{\buildrel{\lower3pt\hbox{$\scriptscripts  tyle\rightharpoonup$}} <br />
\over u} .\mathord{\buildrel{\lower3pt\hbox{$\scriptscripts  tyle\rightharpoonup$}} <br />
\over v} = \alpha
    and :
    <br />
\begin{array}{l}<br />
\alpha :const - value \\ <br />
\mathord{\buildrel{\lower3pt\hbox{$\scriptscriptst  yle\rightharpoonup$}} <br />
\over u} :const - vector \\ <br />
\end{array}
    Shouldn't this work for all vectors?

    Dot products always give a scalar value, so a linear combination of dot products should also be a scalar...
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