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Vectors Question

  1. Sep 28, 2009 #1
    If you are given vector a = axi + ayj + azk and you want to find the magnitude of a, then would you just do the square root of ax2 + ay2? If so, then what about az? What is azk actually? I'm a little unclear about it being related to a.
     
  2. jcsd
  3. Sep 28, 2009 #2

    Delphi51

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    You would do the square root of ax2 + ay2 + ay2.
    Sorry, I don't know how to make superscripts. Too bad they don't copy.
     
  4. Sep 29, 2009 #3
    You mean az for the last one?

    And to do superscripts, just put "[.SUP] [/SUP.]" without the quotations and periods (caps don't matter). And it's for subscripts.
     
  5. Sep 29, 2009 #4

    Delphi51

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    Yes az, and thanks for the tip.
     
  6. Sep 29, 2009 #5
    Just a quick explanation for that azk term, if you still are unclear about it.

    k adds another dimension to the vector. When a vector is only in i,j it's 2D and i,j,k is 3D. See it as drawing it in a xyz-coordinate system instead of a xy one. And as was mentioned earlier, it changes things a little bit when it comes to the magnitude. You wouldn't just do the √(ax2 + ay2), because then you wouldn't take the third dimension into consideration. From there it's not too big of a leap to √(ax2 + ay2 + az2).

    You can prove it using Pythagoras' theroem. If you draw a 3D vector in a coordinate system you can figure it out. It can be a bit tricky to see, but it's not impossible.
     
  7. Sep 29, 2009 #6
  8. Sep 29, 2009 #7

    Delphi51

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    You could do it that way and you'll get the same answer.
    It would be interesting to prove that . . .
     
  9. Sep 29, 2009 #8
    Actually I just realized that the square root of az2 + ay2 is the hypothesis. So I guess it makes sense.
     
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