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Vector components in the 3 dimensions

  1. Sep 2, 2008 #1
    Given F = (-20i + 50j = 10k)

    [​IMG]

    1. The component of the foce projected along the pole AO.
    2. The magnitude of the projected component of the F along the pole AO.

    I have no idea where to begin, I think I need to find the angles but I'm not sure how in three dimensions.


    (please excuse the picture...i know its not the greatest)
     
  2. jcsd
  3. Sep 2, 2008 #2

    tiny-tim

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    Welcome to PF!

    Hi clickcaptain ! Welcome to PF! :smile:

    No, you don't need to find the angles …

    you're thinking of the formula F cosθ for the component of force F in a direction at an angle θ.

    But you can also use the formula F.n, the direct product of the force and the unit vector in that direction …

    and when the question gives you the coordinates, that's a lot easier! :wink:
     
  4. Sep 2, 2008 #3
    so the unit vector would be ...

    position vector of pole = r = 3i - 2j + 6k)
    length of r = l = sqrt(3^2 + 2^2 + 6^2) = 7

    u = r/l = 3/7i - 2/7 j + 6/7 k

    is that right?

    then take that times the force vector given?
     
  5. Sep 2, 2008 #4

    tiny-tim

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    Yup! :biggrin:

    (though I would have waited until the next step before dividing by 7 … :wink:)
    (you mean dot, not times, of course :wink:)

    Yes … that gives you the component of force along that direction. :smile:
     
  6. Sep 2, 2008 #5
    thanks!! :-)
     
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