  A vector balleans is a vector space over $\mathbb{R}$ endowed with a coarse
structure in such a way that the vector operations are coarse mappings. We
prove that, for every ballean $(X, \mathcal{E})$, there exists the unique free
vector ballean $\mathbb{V}(X, \mathcal{E})$ and describe the coarse structure
of $\mathbb{V}(X, \mathcal{E})$. It is shown that normality of $\mathbb{V}(X,
\mathcal{E})$ is equivalent to metrizability of $(X, \mathcal{E})$.
