This paper is devoted to the study of families of tangent lines
to curves in Euclidean three dimensional space by the medium of a
particular representation for lines.
First, a ring of elements called dual numbers is described,
and a vector space over this ring, whose elements are called dual
vectors, is defined.
Next, a subset of the dual vectors is singled out. The members
of this subset are called Study vectors. The set of Study vectors
is shown to be in one-to-one correspondence with the set of all directed
lines in Euclidean three dimensional space. Study vectors are
used to represent the lines to which they correspond.
A necessary and several sufficient conditions on a family of
Study vectors are given in order that they form a family of tangents
to a curve in Euclidean three dimensional space
