\beta_{V},
\odot_{V},\iota_{V}, V_{0}) $ and $ ( W, \alpha_{W}, \beta_{W},
\odot_{W}, \iota_{W}, W_{0}) $. We have that $ V_{0}\times W_{0}$ is a vector subspace of the direct product $ V\times W$ of vector spaces $ V$ and $W$.

We can easy prove that $ V\times W$ endowed with the structure functions $ \alpha_{V\times W}, \beta_{V\times
W}, \odot_{V\times W} $ and $ \iota_{V\times W} $ given by\
$ \alpha_{V\times W}(v,w):=( \alpha_{V}(v), \alpha_{W}(w)),~
\beta_{V\times W}(v,w):=( \beta_{V}(v), \beta_{W}(w)),$\
$(v_{1}, w_{1})\odot_{V\times W} (v_{2}, w_{2}):= ( v_{1}
\odot_{V} v_{2}, w_{1} \odot_{W} w_{2} ), ~ \iota_{V\times W}(v,w):=( \iota_{V}(v), \iota_{W}(w))$\
for all $ v, v_{1}, v_{2} \in V $ and $ w, w_{1}, w_{2} \in W $, is a vector groupoid over $V_{0}\times W_{0}$.

This vector groupoid is called the [*direct product of vector groupoids*]{} $(V,V_{0})$ and $(W,W_{0})$.

By a direct computation we can verify that the projections\
$pr_{V} : V\times W \to V$ and $ pr_{W} : V\times W \to W$ are morphisms of vector groupoids, called the [*canonical projections*]{} of the vector groupoid $ V\times W$ onto vector groupoid $V$ and $ W$, respectively. The following assertion holds

[*The direct product of two transitive vector groupoids is also a transitive vector groupoid*]{}.

[**2. Trivial vector 