Vector Notation, arrow coupled with hat versus hat alone

In summary: I couldn't quite work out why \vec{r} and \hat{\vec{r}} would produce two different results, and I couldn't find any documentation to back me up.In summary, the pdf has vector notation that uses hat notation and the doubled notation.
  • #1
hjel0743
5
0
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

  • magnetic_field_deriv_new.pdf
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  • #2
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
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
In the pdf the doubled notation does not appear to have any special significance.
 
  • #5
The doubled notation in that pdf just means a unit vector (same as the hat by itself).
 
  • #6
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
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.
 
  • #8
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.
 

1. What is vector notation?

Vector notation is a mathematical representation of a vector using arrows and hats. The arrow indicates the direction and magnitude of the vector, while the hat represents the unit vector in that direction.

2. What is the purpose of using an arrow and hat in vector notation?

The arrow and hat in vector notation help to visually represent the direction and magnitude of the vector. This makes it easier to understand and manipulate vectors in mathematical equations.

3. Why is the hat sometimes omitted in vector notation?

The hat is often omitted in vector notation when dealing with unit vectors, as the direction is already implied by the unit vector itself. This simplifies the notation and makes it more concise.

4. Can the arrow and hat be used interchangeably in vector notation?

No, the arrow and hat have different meanings in vector notation. The arrow represents the direction and magnitude of the vector, while the hat represents the unit vector in that direction.

5. How is vector notation used in physics?

In physics, vector notation is used to represent physical quantities that have both magnitude and direction, such as force, velocity, and acceleration. It is also used in vector operations, such as addition and subtraction, to solve problems in mechanics and other areas of physics.

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