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Math Help - [SOLVED] Vector equation for the intersection between surfaces.

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    [SOLVED] Vector equation for the intersection between surfaces.

    Find a vector equation for the intersection of the surfaces x^2+y^2=25 and z=x+y. (Hint: What is the geometric object described by x^2+y^2=25? How can you write that in parametric form?)

    I realize that x^2+y^2=25 is a circle, and I'm pretty sure I have to solve for one of the variables in the second surface and substitute into the first surface, but I don't know where to go after that. Any help would be greatly appreciated!
    Last edited by pedro2208; October 11th 2009 at 07:54 PM.
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  2. #2
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    Quote Originally Posted by pedro2208 View Post
    Find a vector equation for the intersection of the surfaces x^2+y^2=25 and z=x+y. (Hint: What is the geometric object described by x^2+y^2=25? How can you write that in parametric form?)

    I realize that x^2+y^2=25 is a circle, and I'm pretty sure I have to solve for one of the variables in the second surface and substitute into the first surface, but I don't know where to go after that. Any help would be greatly appreciated!
    By your hint note that x^2+y^2=5^2 is an infinite circular cylindar center on the z-axis. In poloar coordinates it has the equation r=5

    Remember that x=r\cos(\theta)=5\cos(\theta) and

    y=r\sin(\theta)=5\sin(\theta) and

    z=x+y=5\cos(\theta)+5\sin(\theta) so finally

    v(\theta)=5\cos(\theta) \vec i +5\sin(\theta) \vec j + (5\cos(\theta)+5\sin(\theta))\vec k
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    Thank you! I completely forgot about changing it to polar coordinates. I appreciate the help!
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