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...