The different kinds of products between two Euclidean vectors may contain 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, $$\vec{u}\!\times\!(r\vec{v}) = (r\vec{u})\!\times\!\vec{v} = r(\vec{u}\!\times\!\vec{v}),$$ and also for dyad product, $$\vec{u}(r\vec{v}) = (r\vec{u})\vec{v} = r(\vec{u}\vec{v}).$$