  This paper deals with skew ruled surfaces $\varPhi$ in the Euclidean space
$\mathbb{E}^{3}$ which are right normalized, that is they are equipped with
relative normalizations, whose support function is of the form $q(u,v) =
\frac{f(u) + g(u)\, v}{w(u,v)}$, where $w^2(u,v)$ is the discriminant of the
first fundamental form of $\varPhi$. This class of relatively normalized ruled
surfaces contains surfaces such that their relative image $\varPhi^{*}$ is
either a curve or it is as well as $\varPhi$ a ruled surface whose generators
are, additionally, parallel to those of $\varPhi$. Moreover we investigate
various properties concerning the Tchebychev vector field and the support
vector field of such ruled surfaces.
