What is the Meaning of Vector Magnitude Symbols?

[CinderBlockFist]

when you use these symbols | |, does that mean absolute value of the vector size (since it is same as absolute value symbols)? Or do they just have a different meaning, that we just write the same symbols. So |U| automatically implies just the magnitude of U?

Also, what is a unit vector e used for? Why do we need to multiply a vector U by this unit vector? If the problem provides me w/ an arrow and vector U = 50 Newtons. Why do I need to multiply it by e? I don't gett it.

 

[jcsd]

Yes |U| (sqrt(<U,U>)) is the magitude or length of a vector and is therefore a scalar. The unit vectors form basis which allows you to define U in terms of scalars (it's components in that basis).

 

[CinderBlockFist]

So the unit vector e is used to break up the vector into components? What if the vector U is given only in vector ie. 50 Newtons w/out any coordinates? BTW thanks for the response

 

[Galileo]

Yes, $|\vec U|$ is just the magnitude of the vector $\vec U$, it's just a (positive) number. (Remember, vectors have both magnitude and direction).
When you're only interested in the magnitude, you use $|\vec U|$.
In mathematics it's more commonly called the 'length' or the 'norm' of the vector and written $||\vec U||$.

Likewise, when you are not interested in the magnitude but only in the direction of the vector, use the unit vector of $\vec U$. It's a vector with length 1 and points in the direction of $\vec U$.
Every vector $\vec U$ can be written as $\vec U=|\vec U|\vec e$, where |$\vec U$| is the magnitude of the vector and $\vec e$ is the unit vector in the direction of $\vec U$.

 

[jcsd]

The unit vector in the direction of U is U/|U|.

 

[CinderBlockFist]

Thanks guys