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Vector calculus, normals to plane curves

  1. Mar 10, 2012 #1
    1. The problem statement, all variables and given/known data
    show that n(t)=-g'(t)i+f'(t)j and -n(t)=g'(t)i-f'(t)j are both normal to the curve r(t)=f(t)i+g(t)j at the point (f(t),g(t)).


    2. Relevant equations



    3. The attempt at a solution
    i tried finding the unit normal of r(t) in hopes that it would be exactly what n(t) and its negative are, but after going through a lot of algebra i didnt get what i was hoping would be the solution, unless i did some algebra mistake. Anyways i doubt im approaching this problem the right way and would just like a hint at what to do.
     
  2. jcsd
  3. Mar 10, 2012 #2

    tiny-tim

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    hi miglo! :smile:

    hint: what is the tangent to f(t)i+g(t)j ? :wink:
     
  4. Mar 10, 2012 #3
    f'(t)i+g'(t)j?
     
  5. Mar 10, 2012 #4

    LCKurtz

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    Yes. Are the supposed normals perpendicular to the tangent?
     
  6. Mar 10, 2012 #5
    yeah i think i just figured it out like a minute ago
    i take the dot product of r'(t) with n(t) which equals 0, therefore n(t) is normal to the curve at (f(t),g(t)) and then i do the same with -n(t)
     
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