# Symbolic represenation of the unit vector and the vector

1. Sep 3, 2007

### Helicobacter

1. Is v-hat a unit vector or a vector?

If it is a unit vector how do you symbolically represent a vector?
If it is a vector how do you symbolically represent a unit vector?

2. Is v-hat the same thing as v with an arrow over it?

2. Sep 3, 2007

### ice109

usually things with a hat are unit vectors, bolded letters or letters with arrows on top are regular vectors

3. Sep 3, 2007

### Staff: Mentor

To be a bit flip, yes. A unit vector is a vector. Specifically, it is a vector with unit length.

In terms of vector analysis, the hat symbol place over some other symbol almost exclusively denotes that the quantity in question is a unit vector. Since a unit vector is a special kind of vector, you don't really need to be verbose and say it is a vector as well. That said, some use bold symbols to represent vectors, and a unit vector is a represented as a bold symbol with a hat over it.

These two statements indicate you are having a bit of a confusion regarding what constitutes a vector. A vector is some thing with a magnitude and a direction. A unit vector is a vector with unit magnitude.

No. A v with an arrow over it connotes a vector, period. It might have magnitude 20, 1/20, whatever.

4. Sep 3, 2007

### Helicobacter

My textbook uses only boldface w/o hats to denote unit vectors :/

Why don't they standardize these things? Derivative symbol, vectors,...-it's a total chaos

5. Sep 3, 2007

### Staff: Mentor

I've seen many schemes before, but never that one. I suppose the authors have their reasons. Personally, yech.

People can get downright religious regarding nomenclature. For example, the authors of your text must love this scheme. People tend to abandon their idiosyncratic ways when they are ridiculed enough. Having enough instructors stop using their texts because of the idiosyncratic notations helps. Until then, the poor students are stuck with it.

6. Nov 19, 2009

### vineet.kvbgh

I wanted to know why shall we give a hat over a vector?why shall we change our arrow?what is the need?

7. Nov 19, 2009

### HallsofIvy

Staff Emeritus
Is your text using the "hat" for all unit vectors or is it using that notation specifically to distinguish basis vectors? That would make a lot more sense. In any case, there is no deep mathematical distinction between vectors in general and "unit" vectors or "basis" vectors. There may be some convenience in a particular application in distinguishing them.

8. Nov 20, 2009

### LCKurtz

Of course, if you are in front of a class, you don't have the option of bold-face chalk. So $\vec u$ and $\hat u$ are pretty convenient notations.

9. Nov 21, 2009

### vineet.kvbgh

no,u didn't understood me.I wanted to know that why are unit vectors are given a hat over them?i.e. We were using vectors by giving an arrow over it then why suddenly a hat was introduced for unit vectors?what if we use the same arrow for unit vectors also.

10. Nov 21, 2009

### HallsofIvy

Staff Emeritus
I have never seen a text use a "hat" to distinguish unit vectors. I have seen that used (mostly in physics texts) to distinguish vectors in a particular basis. And they do that, of course, to make it clear that these are basis vectors, as opposed to general vectors.

11. Nov 21, 2009

### LCKurtz

I think that notation is a bit more common. A quick google search finds this text:

12. Nov 21, 2009

### Staff: Mentor

The usage of hats to denote unit vectors, regardless of the basis, is widely used among physicists.