  We extend the notion of singular vectors in the context of Diophantine
approximation of real numbers with elements of a totally real number field $K$.
For $m\geq1$, we establish a version of Dani correspondence in number fields
and prove that under a class of `friendly measures' in $K_S^m$, the set of
singular vectors has measure zero. Tackling the inheritance question, we show
the existence of nondegenerate divergent orbits on manifolds in $K_S^m$ under
the action of a certain one parameter subgroup of $\mathrm{SL}_{m+1}(K_S)$.
