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Homework Help: Vector parameterization of intersection of 2 surfaces

  1. Sep 15, 2010 #1
    1. The problem statement, all variables and given/known data
    Find a vector parameterization of the intersection of the surfaces x2+y4+2z3=6 and x=y2 in R3.

    3. The attempt at a solution

    I let x=t.
    Then y3=t

    I solved the first equation for z in terms of x
    z = cube root ((t2+(t(cube rt(t)) - 6)/-2)

    I know this is wrong because I checked the back of the book, but I'm not sure how to do it correctly.
    Thank you!
  2. jcsd
  3. Sep 15, 2010 #2


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    Is your 2nd surface [itex]x=y^2[/itex] or [itex]x=y^3[/itex]?

    In either case, to avoid taking sqare roots and cube roots of stuff, try letting [itex]y=t[/itex] instead and solving for x.
  4. Sep 15, 2010 #3
    x=y3, sorry.

    So, when y=t, x=t3
    and z= cube rt ((-1/2)(t6+t4-6))

    This is still wrong. The answer is <t2,t,cube rt(3-t4)>
    It doesn't help that I know the answer unless I know how to do it, though.
  5. Sep 15, 2010 #4


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    Judging from the answer, it looks as though the 2nd surface is supposed to be [itex]x=y^2[/itex], so I'd double check the question if I were you.
  6. Sep 15, 2010 #5
    thank you. you were right, it was x=y^2.
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