In English, a vector is said to have two properties: a length and a direction. The possible directions correspond to half-lines out of the origin (so that, eg, up and down are different directions). In many other languages, a vector is said to have three properties: directions correspond to lines (so that a vector pointing up and one pointing down have the same up-down direction), and a third property determines which way the vector is pointing along that line (up or down in our example).
This may seem strange at first, but it's actually very useful to separate these concepts in mathematics. In fact, I need to do it in something I'm writing right now, but I can't find the right English words for it.
Firstly, I need a word to indicate that third property. Is there any accepted term for it? In the wikipedia article on vectors, there is a picture where it is labeled as "sense", although the term does not occur anywhere in the article itself.
Secondly, I might need a clear way to indicate which sense of the word "direction" I'm using (line or half-line). This does not need to be a single word, but it should be as clear and unambiguous as possible.
It would be even better if any official references for this usage could be found. This problem is bound to have come up before in the translation of foreign scientific literature.