Find all vector

**dhiab** · January 9th 2010, 08:02 PM

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

such that :

$\mathord{\buildrel{\lower3pt\hbox{$\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 :
$ \begin{array}{l} \alpha :const - value \\ \mathord{\buildrel{\lower3pt\hbox{$\scriptscriptst yle\rightharpoonup$}} \over u} :const - vector \\ \end{array}$

**Prove It** · January 9th 2010, 08:20 PM

Originally Posted by dhiab

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

such that :

$\mathord{\buildrel{\lower3pt\hbox{$\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 :
$ \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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