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Math Help - Calculus III: Vector Functions and Space Curves

  1. #1
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    Angry Calculus III: Vector Functions and Space Curves

    If someone could please help me with this problem it would be most appreciated! I don't even know where to start!

    Find a vector function that represents the curve of intersection of the two surfaces (in the 3D space):

    The paraboloid: z = 4x^2 + y^2
    The parabolic cylinder: y = x^2
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  2. #2
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by saxyliz View Post
    If someone could please help me with this problem it would be most appreciated! I don't even know where to start!

    Find a vector function that represents the curve of intersection of the two surfaces (in the 3D space):

    The paraboloid: z = 4x^2 + y^2
    The parabolic cylinder: y = x^2
    plug in y = x^2 into z, so that z = 4x^2 + x^4

    now parametrize the curve using x = t as the parameter
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  3. #3
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    What exactly do to mean by "parametrize the curve?"

    Is it:
    z = 4t^2 + t^4
    ?
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  4. #4
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by saxyliz View Post
    What exactly do to mean by "parametrize the curve?"

    Is it:
    z = 4t^2 + t^4
    ?
    the vector function is r(t) = \left< x(t), y(t), z(t) \right> = \left< t, t^2 , 4t^2 + t^4 \right>
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  5. #5
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    Oh! I get it now! Thanks a lot!
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