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Representing a graph by a Vector-Valued Function

  1. Sep 30, 2012 #1
    1. The problem statement, all variables and given/known data
    Sketch the space curve represented by the intersection of the surfaces. Then represent the curve by a vector-valued function using the given parameter.


    2. Relevant equations
    z = x^2 + y^2, x + y = 0, x = t


    3. The attempt at a solution
    Space curve sketched (elliptic paraboloid corresponding to z-axis)
    Vector valued function: x = t, y = -t; z = t^2 + (-t)2; z = 2t^2; r(t) = ti - tj + 2t^2k

    **Intersection of the surface, not sure how to obtain this. I have the feeling once I get it I'm gonna be shaking my head for having forgotten something. So I've tried setting
    x^2 + y^2 = x + y
    tried substituting in t for x and y values
    tried reverse engineering what I'm supposed to do with the answers plugged in to the equations.
    tried finding x int, y int, and z int.

    Just don't know how to procede. Any assistance is greatly appreciated.
     
  2. jcsd
  3. Sep 30, 2012 #2

    Dick

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    If x=t and x+y=0, what is y in terms of t? Now what is z in terms of t? It is really simple.
     
  4. Oct 1, 2012 #3
    I already have the vecor valued function. I'm looking for the points of intersection. How do I find that the surfaces intersect at ((root2), -(root2), 4)?
     
  5. Oct 1, 2012 #4

    Dick

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    You already have the curve that represents the intersection of the two surfaces. The point you give is just one point on that intersection curve. (1,-1,2) is another. There are an infinite number of them, every value of t gives a different one. Are you intersecting that curve with something else that makes t=sqrt(2) special?
     
  6. Oct 1, 2012 #5
    ok thanks. Sounds like I wasted a lot of my time, and potentially yours as well as some bandwidth. Thanks again for your time.
     
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