Geometric classification of orbits of a family of Killing vector fields in Euclidean spaces

Let $D \subset V(M) $ be a family of smooth vector fields defined on a manifold $M$. We examine properties of orbits of a family of Killing vector fields in Euclidean spaces and prove the existence of two Killing vector fields in Euclidean spaces such that the orbit of a family consisting of these vector fields covers the whole Euclidean space. A classification of orbits of Killing vector fields in Euclidean spaces is given.