Directed line segments in Euclidean space

Question

Let $(\mathbb R^3,d)$ where $d$ is Euclidean distance be called Euclidean space.

For any two points $a,b \in \mathbb R^3$, let the set ${\{s:s=ta+(1-t)b:0 \leq t \leq 1}\}$ be called line segment from $a$ to $b$.

In this context, how are directed line segments defined?

Answer 1

One could define a directed line segment to be an ordered triple $$\vec{ab} = (a,b,\overline{ab}) $$ where $\overline{ab}$ is the set that you defined.