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Is this ok with Polar coordinates?

  1. Oct 24, 2008 #1
    1. The problem statement, all variables and given/known data

    we have this diagram were it says that the change in the unit vector der equals in magnitude the change in the angle betwen the two unit vectors er. Could someone explain me why is this?

    I include the diagram named Polar coordinates.
     

    Attached Files:

  2. jcsd
  3. Oct 24, 2008 #2
    I don't think de_r is a unit vector. It is the difference between two unit vectors, but it itself is not a unit vector.
     
  4. Oct 24, 2008 #3
    He doesn't say that de_r is a unit vector, it's the *change* in a unit vector.

    But to answer the original question: yes, if you consider |e_1-e_2|^2 and use that e_1 is only a little (infinitesimally) different from e_2, e_1=e_2+\delta e, then you'll find what you need by comparing the answer to e_1\cdot e_2, and using how the angle between two vectors relates to the angle between the vectors, and Taylor expanding the cosine for small angles.
     
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