Is "alignment" (or something else) a better word than "direction" for a senseless direction? When I encountered the concept of direction being prior to the ordering of points on a line representing (parallel to) the direction, I thought it was a valuable distinction.  I resolved to keep this distinction in my work.  But that didn't last very long.

While taking notes on Schouten's Tensor Analysis book, I found myself writing things like: there is a sense in which a line segment determines a direction without a sense.  A sense is determined by a ray.  So in order to talk about a line having a direction in the naive sense, we have to assign a sense to a senseless line. ... ad nauseam.

It gets even worse when we talk about directed flat p-manifolds in $E_n.$  

While pondering this predicament, I came upon the ideal of saying that a line determines an alignment, which when a relative ordering of points on the line is additionally specified, determines a direction.

Is the term alignment or some other, similar term ever used to denote the idea of direction without sense?

Is the term alignment used in mathematics in a way that would conflict significant with my proposed usage?
Maybe oriented is the word you are looking for?
I'd get in the word "colinear"/"colinearity".

--- rk