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Thread: Find all vector

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

    Find all vector
    $\displaystyle {\mathord{\buildrel{\lower3pt\hbox{$\scriptscripts tyle\rightharpoonup$}}
    \over v} }
    $


    such that :

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


    such that :

    $\displaystyle \mathord{\buildrel{\lower3pt\hbox{$\scriptscriptst yle\rightharpoonup$}}
    \over v} .\mathord{\buildrel{\lower3pt\hbox{$\scriptscripts tyle\rightharpoonup$}}
    \over v} + 2\mathord{\buildrel{\lower3pt\hbox{$\scriptscripts tyle\rightharpoonup$}}
    \over u} .\mathord{\buildrel{\lower3pt\hbox{$\scriptscripts tyle\rightharpoonup$}}
    \over v} = \alpha $
    and :
    $\displaystyle
    \begin{array}{l}
    \alpha :const - value \\
    \mathord{\buildrel{\lower3pt\hbox{$\scriptscriptst yle\rightharpoonup$}}
    \over u} :const - vector \\
    \end{array}$
    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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