Vector Notation, arrow coupled with hat versus hat alone

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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!
 

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  • #2
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Hats traditionally denote unit vectors--[itex]\hat r = \vec r /|\vec r|[/itex]. It's rare that one would hat a vector and also draw the overline.
 
  • #3
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I was wondering about that... Can you think of what the two coupled together would mean though? I can't find any supporting literature.
 
  • #4
Simon Bridge
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In the pdf the doubled notation does not appear to have any special significance.
 
  • #5
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The doubled notation in that pdf just means a unit vector (same as the hat by itself).
 
  • #6
Simon Bridge
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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 ;)
 
  • #7
pwsnafu
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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.
 
  • #8
Simon Bridge
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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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