  For vectors in $\mathbb{E}_3$ we introduce an associative, commutative and
distributive multiplication. We describe the related algebraic and geometrical
properties, and hint some applications. Based on properties of hyperbolic
(Clifford) complex numbers, we prove that the resulting algebra $\mathbb{T}$ is
an associative algebra over a field and contains a subring isomorphic to
hyperbolic complex numbers. Moreover, the algebra $\mathbb{T}$ is isomorphic to
direct product $\mathbb{C} \times \mathbb{R}$, and so it contains a subalgebra
isomorphic to the Gaussian complex plane.
