scalar factor transfer rules

The different kinds of products between two Euclidean vectors may an additional scalar as factor in either vector factor $\overrightarrow{u}$, $\overrightarrow{v}$.  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,

$$\overrightarrow{u}\cdot (r\overrightarrow{v})=(r\overrightarrow{u})\cdot \overrightarrow{v}=r(\overrightarrow{u}\cdot \overrightarrow{v}),$$

for vector product,

$$\overrightarrow{u}\times (r\overrightarrow{v})=(r\overrightarrow{u})\times \overrightarrow{v}=r(\overrightarrow{u}\times \overrightarrow{v}),$$

and also for dyad product,

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