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Equations for normal, osculating, and rectifying planes

  1. Oct 13, 2011 #1
    We are being asked to find the eq's for normal, osculating, and rectifying planes for the following equation:
    r(t) (cos t)i + (sin t)j - k @ t=pi/4
    I have already found the following:
    T(pi/4) = (-√2/2)i + (√2/2)j = 0k

    N(pi/4) = (-√2/2)i + (-√2/2)j + 0k

    B = 0i + 0j + k

    But, I don't know where to start for those three equations.
  2. jcsd
  3. Oct 13, 2011 #2


    Staff: Mentor

    Should be r(t) = ...
    Should be T(pi/4) = (-√2/2)i + (√2/2)j + 0k

    Note that I didn't check your math, just obvious typos.

    Try this link to a wikipedia page that discusses these planes- http://en.wikipedia.org/wiki/Frenet–Serret_formulas. You have all three vectors, so getting an equation of any of the three planes should be easy, since you have a normal to the plane and can easily get the point that's on all three planes (the point at r(pi/4)).
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