Vector Notation, arrow coupled with hat versus hat alone

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Discussion Overview

The discussion revolves around the notation used for vectors, specifically the use of hats and arrows in vector representation. Participants explore the implications of using both notations simultaneously, the traditional meanings of each, and their applications in typesetting and literature.

Discussion Character

  • Technical explanation, Conceptual clarification, Debate/contested

Main Points Raised

  • One participant questions the meaning of using both hats and arrows on vectors, suggesting that hats denote vector components and expressing uncertainty about taking dot products between components and full vectors.
  • Another participant clarifies that hats traditionally denote unit vectors, indicating that it is uncommon to use both notations together.
  • Some participants speculate on the significance of the combined notation, with one noting that it appears to have no special meaning in the referenced document.
  • Discussion includes historical perspectives on vector notation, mentioning that boldface was traditionally used for vectors while hats indicated unit vectors.
  • Participants share insights on typesetting practices in LaTeX, noting that different styles may lead to confusion regarding unit vector representation.
  • There is mention of alternative notations, such as under-squiggles and under-half-arrows, which were used in the past to denote vectors in handwriting.

    • Areas of Agreement / Disagreement

    Participants express differing views on the implications of using both hats and arrows, with no consensus reached on the significance of this notation. The discussion remains unresolved regarding the specific meanings and applications of the combined notation.

    Contextual Notes

    Participants note that the discussion is influenced by historical practices and typesetting conventions, which may not be universally applicable or understood in current contexts.

hjel0743
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I've attached the .pdf from which I have questions.

After it says "Take the square of the numerator" halfway down the page, there is an equation that lists vector components with hats and arrows at the same time, and the arrow on other vectors. Can someone help explain the difference to me?

I had though hats denoted vector components, but I don't think you can take the dot product of a component and a full vector. Please correct me if I'm wrong!
 

Attachments

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Hats traditionally denote unit vectors--\hat r = \vec r /|\vec r|. It's rare that one would hat a vector and also draw the overline.
 
I was wondering about that... Can you think of what the two coupled together would mean though? I can't find any supporting literature.
 
In the pdf the doubled notation does not appear to have any special significance.
 
The doubled notation in that pdf just means a unit vector (same as the hat by itself).
 
Used to be that all vectors would be bold-face and unit vectors would be denoted by the hat as well ... if you were to write it in LaTeX (for example) you used to have to write \hat{\vec{r}} with the \vec{r} giving you the boldface.

Update the style without updating the markup and you get doubled notation.

I think there is also something about whether you use the hat with the i,j,k Cartesian unit vectors.

Of course, some of us come from the time when an under-squiggle or an under-half-arrow was common ;)
 
Simon Bridge said:
Of course, some of us come from the time when an under-squiggle or an under-half-arrow was common ;)

The "under-squiggle" is used to tell the typesetter to use boldface. That why vectors in handwriting are denoted with them. But you don't use it with LaTeX.
 
Oh that's where it comes from? I see lots of people freehand the overarrow these days.

And no, like I said, you use the \vec markup for vectors (and, fwiw, \bf or \mathbf for bold face). The \vec is so that the vectors get whatever typesetting the journal wants to put there ... it had not occurred to me before that there could be a problem between two styles for unit vectors... not a big problem admittedly... and it may not be what happened here :)

Another discussion about vector notation:
https://www.physicsforums.com/showthread.php?t=565882
... I had a bit of a bee in my bonnet about this at one stage.
 

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