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Parametric surfaces

  1. Sep 28, 2015 #1
    1. The problem statement, all variables and given/known data

    upload_2015-9-28_20-3-38.png
    2. Relevant equations
    upload_2015-9-28_20-5-32.png

    3. The attempt at a solution
    so to start this off, I choose a random point, by setting u and v = 0

    giving me the point (0,3,1) but I have no idea how what to do next.

    how do I find ua and vb?
     
  2. jcsd
  3. Sep 28, 2015 #2
    Thinking directly, ##a## and ##b## must be to vectors lying on the plane. Maybe you can set they start at ##r_0,## that is your ##(0,3,1)## and find any two independent vector to structure the plane.
     
  4. Sep 28, 2015 #3
    sorry, a bit confused. do I plug in more numbers for v and u?
     
  5. Sep 28, 2015 #4
    ##v## and ##u## then are parameter. Selected ##a## and ##b## will dominate the form of the plane.
     
  6. Sep 28, 2015 #5

    Ray Vickson

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    If ##(x,y,z)## are the cartesian coordinates of a point on the surface, how do you express the values of ##x##, ##y## and ##z## in terms of the parameters ##u## and ##v##? Can you use those expressions to re-write the surface in the form ##z = a + b x + cy##?
     
  7. Sep 28, 2015 #6
    how did you think of the form ##z = a + b x + cy##? does the surface have to be in that form?
     
  8. Sep 28, 2015 #7
    anyway, the textbook came up with upload_2015-9-28_20-3-38-png.89508.png = <0,3,1> + u<1,0,4> + v<1,-1,5> and I have no idea how they came up with u<1,0,4> and v<1,-1,5>.

    how are they coming up with vectors with just a given point?!
     
    Last edited: Sep 28, 2015
  9. Sep 28, 2015 #8

    Ray Vickson

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    What are ##\bf{i}, \bf{j}## and ##\bf{k}##?
     
  10. Sep 28, 2015 #9
    i = <0,3,1>
    j= u<1,0,4>
    k=v<1,-1,5>
     
  11. Sep 28, 2015 #10
    They are unit vectors on the three dimension instead of what you say. The solution makes it to the form to match the required.
     
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