# scalar factor transfer rules

The different kinds of products between two Euclidean vectors may an additional scalar as factor in either vector factor $\vec{u}$, $\vec{v}$.  Then such a scalar $r$ can be transferred from a vector to the other vector and to the whole product.  This is true for scalar product,

 $\vec{u}\!\cdot\!(r\vec{v})=(r\vec{u})\!\cdot\!\vec{v}=r(\vec{u}\!\cdot\!\vec{v% }),$

for vector product,

 $\vec{u}\!\times\!(r\vec{v})=(r\vec{u})\!\times\!\vec{v}=r(\vec{u}\!\times\!% \vec{v}),$

 $\vec{u}(r\vec{v})=(r\vec{u})\vec{v}=r(\vec{u}\vec{v}).$