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Elimating parameters

  1. Mar 9, 2010 #1
    1. The problem statement, all variables and given/known data
    Eliminate the parameters u and v to obtain a Cartesian equation, thus showing that the given vector equation represents a portion of the surface named. Also, compute the fundamental vector product dr/du x dr/dv in terms of u and v.

    2. Relevant equations

    r(u,v) = asinucosvi + bsinusinvj + ccosuk

    3. The attempt at a solution

    I can find the cross product easy enough(abcsinu((sinucosv/a)i+(sinusinv/b)j+(cosu/c)k), but how should I go about getting rid of the parameters?
  2. jcsd
  3. Mar 9, 2010 #2


    Staff: Mentor

    Let x = asinu*cosv, y = bsinu*sinv, and z = ccosu.

    You can combine x and y by using the identity sin^2(t) + cos^2(t) = 1. That's where I would start.
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