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Surfaces in Space / Vector-Valued Functions

  1. Feb 19, 2009 #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.


    2. Relevant equations

    Surfaces: z=x2+y2, x+y=0
    Parameter: x=t


    3. The attempt at a solution

    So, I sketched the space curve represented by the intersection of the two curves. It's simply a parabola. However, I can't seem to think of how to put it into a vector-valued function. I'm getting a mind block. (Perhaps, before anyone answers this, I may come up with the answer.)
     
  2. jcsd
  3. Feb 19, 2009 #2

    Dick

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    Got it yet? You already have x=t. What's y in terms of t? (Put x=t into the plane equation). Finally z=?
     
  4. Feb 19, 2009 #3
    So, it's just z=t2+(-t)2? and..no I didn't get it yet. I put down my math and did other things. Thanks =) So, it's r(t)=<t,-t,2t2>?
     
    Last edited: Feb 19, 2009
  5. Feb 19, 2009 #4

    Dick

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    Yes, that's z.
     
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