1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Homework Help: 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


    User Avatar
    Science Advisor
    Homework Helper

    hi miglo! :smile:

    hint: what is the tangent to f(t)i+g(t)j ? :wink:
  4. Mar 10, 2012 #3
  5. Mar 10, 2012 #4


    User Avatar
    Science Advisor
    Homework Helper
    Gold Member

    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)
Share this great discussion with others via Reddit, Google+, Twitter, or Facebook