I need complementary explanations for some basic definitions I encountered during introductory Geometry works.
My first question:
Given $V$ any vector space over a field $\mathbb{F}$, when we cite any element $P$ of $V$, does it naturally define a vector $OP$? or does it define just a point in the Space?
My second question:
When we speak of line segments, e.g. $t_1 P_1 + t_2 P_2$ with $t_1 + t_2 = 1$ where $t_{i=1,2}$ are scalars, has this line segment any sense of orientation it implies in the Space?
Thanks.