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Semantics question about vectors

  1. Dec 19, 2015 #1
    Hi all. I have a question that is more about definitions or language, rather than physics.

    So (Euclidean) vectors used in Physics are "geometrical entities endowed with a magnitude and a direction".
    At least this is what i find if I look up "vector" in english speaking websites.
    My "problem" is that in Italy a vector is an object that is fully characterized by three rather than two properties (I think that the same is true in France).
    The point is that "direction" means basically the line which the vector lies on, with no information about the "course" along that line. So both a vector and its opposite have the same direction in Italy, and you need to specify which way they point along that line, to completely define either of them. Hence the three properties: "intensità" (magnitude), "direzione" (the straight line) and "verso" (the "course" along that line).

    I guess that the use of "direction" to denote an undirected line comes from pure mathematics or geometry. I think it has to do with the fact that two points select a straight line irrespective of the order, so lines do not have a direction.

    Still, I am curious as to what would the correct English term be for "the way you can point along a straight line".
    I used "course" above, but it is just a guess. Another guess would be "wise", like in clockwise... But I do not think that it is used by itself, with this meaning.

    I know, sounds like a kind of idle question, but I'm curious.
    Also, since part of the last-year physics classes are taught in English, I sort of need the word to provide a more accurate explanation. After years of hearing that a vector is characterized by three properties, italian are surprised that "english vectors" are characterized by just two properties.

    Thanks a lot
  2. jcsd
  3. Dec 19, 2015 #2


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    Staff: Mentor

    In American English generally (including physics), "direction" normally includes "the way you can point along a straight line." When we say a vector has magnitude and direction, there is no ambiguity in the direction.

    If I wanted to refer to the "direction" of a straight line without specifying "which way", I would probably say "orientation", not "direction."
  4. Dec 19, 2015 #3
    that makes me think
    [itex]\vec{AB} = \vec{BA}[/itex]
  5. Dec 19, 2015 #4
    Yes of course. I entirely understand that, and I agree that it is more practical and intuitive.

    Thanks! I did not think of that! Of course, I think orientation is the word I was looking for!
  6. Dec 19, 2015 #5
    Yes, I know. But that's because what you call "direction" includes both the straight line identified by the vector (that is the same for both [itex]\vec{AB} [/itex] and [itex]\vec{BA} [/itex]) and the orientation onto it (that is different).

    I guess that our use comes from the fact that a vector is an oriented segment (of course, there's the word "orientation" again).
    As long as you think of segments, it is indeed true that [itex]AB=BA [/itex]. In order to tell apart the two vectors associated to the same segment you need to specify their orientation.

    Also, one can (loosely?) talk of the direction of a line. For instance, one way of defining parallel lines is to say that they have the same direction. But then I guess one should say, "the same direction or opposite directions". Or intruduce the concept of "antiparallel", which of course makes sense with vectors.

    Again, this to some extent a matter of language and perhaps tradition, and I agree that our usage is overly mathematical, and your "direction" is more practical and intuitive than ours.
    But of course both work, as long as the notation is clearly stated. Generations of Italian (and French?) physicists have been raised with the notion of vector I'm referring to, and they are not that bad at physics :)
  7. Dec 19, 2015 #6


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