Unit vectors and vector quantities (notation)

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Discussion Overview

The discussion revolves around the notation used for vector quantities, specifically the use of unit vectors and the conventions for indicating vectors, such as the use of arrows or bolding. Participants explore the implications of different notational standards and their preferences in various contexts.

Discussion Character

  • Technical explanation
  • Debate/contested

Main Points Raised

  • Some participants question whether an arrow is necessary on top of vector quantities when using unit vectors, noting that their textbook does not bold them.
  • One participant asserts that a unit vector is still a vector and must be labeled as such, either by bolding or using arrow notation.
  • Another participant mentions that different notations for vectors are interchangeable unless specified otherwise, citing international standards that prefer bold-face for printed material and underscored tildes for freehand writing.
  • There is a mention of LaTeX's default use of overscored arrows, which some participants feel is becoming more common, while others prefer the tilde for speed of writing.
  • One participant highlights that context is crucial for understanding whether a quantity is a vector or scalar, even if the notation does not explicitly indicate it.

Areas of Agreement / Disagreement

Participants express differing preferences for vector notation, with no consensus on a single standard. The discussion reflects a variety of practices and opinions regarding the use of arrows, bolding, and tildes in representing vectors.

Contextual Notes

Participants reference international standards and personal preferences, indicating that notation may vary by region and context. There is also mention of the importance of context in interpreting vector and scalar quantities, which may not always be clear from notation alone.

Who May Find This Useful

This discussion may be useful for students and educators in physics and mathematics, particularly those interested in notation conventions and their implications in academic settings.

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When you write vector quantities with unit vectors, do you still have to draw an arrow on top to indicate that it's a vector? e.g. velocity and acceleration. My textbook doesn't have it bolded so does that mean they're just taking the magnitude and then multiplying by the unit vector to make it a vector?

Also, is there a difference between the tilde on the bottom and arrow on top notation? My math class uses tildes for all vectors. Should you use tildes or arrows with unit vectors?

Thanks
 
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A unit vector is just that, a vector. So it has to be labeled as such, either by bolding it or by an arrow notation. The magnitude is a scalar so it does not.
 
The different ways of writing the vector are interchangeable - so there is no difference implied in the notation unless they tell you there is one. As for which you should use:

International Standards:
ISO 31-11 describes the international standards for math notations ... the standard is bold-face and upright (i.e. not italic) for printing and an underscored tilde freehand. I know there are a lot of US folk who prefer the over-scored arrow ... ISO 31-11 has this as an alternate.

LaTeX defaults to the overscored arrow - and that one seems to be replacing ISO31-11 more and more these days. I personally find the tilde faster to write so that's what I use when I have a choice. In printed material I use LaTeX so...

It's been discussed before.

Don't sweat the changes in notation: use the one you will be assessed in.

If your text uses bold-face for vectors, then v is velocity and v is speed. A unit vector will usually be explicit as in -vj meaning speed v in the -y direction, but it may be implicit like when they say "ship A travels at speed U due north" ... see there is no bold-face but a vector has been described to you. Also notice that scalars are usually italic.

General physics students are expected to glean a lot from context - you'll get the hang of it.
 
Thank you!
 
No worries.

I had a math prof who always used lower-case Greek letters for vectors and Latin characters for scalars. It was great for saving writing. However his work didn't have to represent anything...
 

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