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Vector Magnitude symbols?

  1. Sep 18, 2004 #1
    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 dont gett it.
     
  2. jcsd
  3. Sep 18, 2004 #2

    jcsd

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    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).
     
  4. Sep 18, 2004 #3
    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
     
  5. Sep 18, 2004 #4

    Galileo

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

    Likewise, when you are not interested in the magnitude but only in the direction of the vector, use the unit vector of [itex]\vec U[/itex]. It's a vector with length 1 and points in the direction of [itex]\vec U[/itex].
    Every vector [itex]\vec U[/itex] can be written as [itex]\vec U=|\vec U|\vec e[/itex], where |[itex]\vec U[/itex]| is the magnitude of the vector and [itex]\vec e[/itex] is the unit vector in the direction of [itex]\vec U[/itex].
     
  6. Sep 18, 2004 #5

    jcsd

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    The unit vector in the direction of U is U/|U|.
     
  7. Sep 18, 2004 #6
    Thanks guys
     
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