1. ## 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$}} \over u} :const - vector \\ \end{array}$

2. Originally Posted by dhiab
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...