Unit vectors and vector quantities (notation)

[autodidude]

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

 

[Vorde]

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.

 

[Simon Bridge]

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.

 

[autodidude]

Thank you!

 

[Simon Bridge]

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...