Symbolic represenation of the unit vector and the vector

[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?

 

[ice109]

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

 

[D H]

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

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.

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?

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.

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

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

 

[Helicobacter]

Thanks for your responses!

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

 

[D H]

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

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

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

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.

 

[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?

 

[HallsofIvy]

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.

 

[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.

 

[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.

 

[HallsofIvy]

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.

 

[LCKurtz]

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.

I think that notation is a bit more common. A quick google search finds this text:
http://books.google.com/books?id=cu...6AEwBw#v=onepage&q=unit vector symbol&f=false

 

[D H]

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.

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