# What is the sense of a vector?

Is the sense the same thing as the direction of a vector? If yes, why should we use the term sense instead of direction?

Can anyone illustrate it?

Have a look at this article on vector algebra. In this context sense is a technical term. The relevent extracts from the article are:

Vectors are quantities that require the specification of magnitude, orientation, and sense. The characteristics of a vector are the magnitude, the orientation, and the sense.

The orientation of a vector is specified by the relationship between the vector and given reference lines and/or planes.

The sense of a vector is specified by the order of two points on a line parallel to the vector.

Orientation and sense together determine the direction of a vector.

So the orientation tells you what angle the vector is and the sense tells you which way it's pointing.

• @user146181: Yes. But you should note that the article I linked was (probably) written by a mathematican. I've never heard a physicist use the term sense - we just talk about direction. It isn't obvious to me why you would decompose direction into orientation and sense, though I'm sure there is a good reason. Maybe you should ask in the MathSE. Aug 23, 2014 at 6:41
• For us physicists it's habit to say "magnitude and direction". But we do use the concept of sense without calling it that. Consider flux: we first create an oriented plane segment. Then we assign a sense to it. Passing through one way gives positive flux, the other negative. Offhand I can't think of an analog of that example for oriented line segments, so I see your point. But still, the three words describe different attributes. I tend to describe vectors to students using that language so that it will be in their mind should they go on to higher math. Aug 23, 2014 at 11:14
• @garyp Area is a pseudovector, though, isn't it? I've seen "sense" used for pseudovectors as an indicator that the direction is really just a stand-in for a choice of plane orientation. That wouldn't apply to a true vector like an oriented line segment, though. May 12, 2017 at 4:25
• @garyp Yeah, I believe we're talking about the same thing, I just tend to call it a pseudovector while you call it a bivector. May 12, 2017 at 17:18
• @ZakC Possibly, but the concepts of magnitude, orientation, and sense work in higher dimensions, so they are more general. For vectors in two or three dimensions we might be able to come up with a scheme that works, and that's fine. But it's useful and more satisfying to have more general concepts. Nov 15, 2017 at 14:32

The term "direction" was probably not the best choice of words. Consider this example - a car travelling at 30mph down Smith Street, heading west. Smith Street becomes the direction (or the defined path), west becomes the sense. Simply saying "30mph down Smith Street" would not be enough information. It all comes down to a poor choice of words (or change of meaning over time or a poor translation). In that regard, "orientation" is a better choice than "direction".

The term "sense" in the context of mathematics gives a sign (positive or negative) to a real number. The "sense" is the resultant value of the signum function.

The term "vector direction" describes which way the vector is pointing when described on a two-dimensional coordinate plane. Assuming a vector is only being described in a two-dimensional coordinate system (x-axis and y-axis), the term "vector sense" further describes vector direction by giving the vector direction a sign (positive direction or negative direction).

The term "orientation" in the context of mathematics refers to the positioning of points in relation to one another following a transformation or rotation of a geometric figure.

The term "vector orientation" further describes the vector sense and is required if the vector is described on more than two axes (x-axis and y-axis).