# Thread: Find all vector

1. ## Find all vector

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}$

2. 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...