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Math Help - [SOLVED] intersection between cylinder & plane

  1. #1
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    [SOLVED] intersection between cylinder & plane

    Find a vector function that represents the curve of intersection of the cylinder x^2+y^2=16 and plane x+z=5.

    I am stuck. I setting the equation equal to eachother but i could not solve for anything or get anything useful out of it.

    I believe I am supposed to project the cylinder down so its a circle on the xy plane and then find the ellipse that the intersecion makes but i cannot figure out how.

    Any help would be appreciated.
    Last edited by snaes; September 23rd 2009 at 05:37 PM. Reason: make fancy equations with [math]
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  2. #2
    Super Member redsoxfan325's Avatar
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    Quote Originally Posted by snaes View Post
    Find a vector function that represents the curve of intersection of the cylinder x^2+y^2=16 and plane x+z=5.

    I am stuck. I setting the equation equal to eachother but i could not solve for anything or get anything useful out of it.

    I believe I am supposed to project the cylinder down so its a circle on the xy plane and then find the ellipse that the intersecion makes but i cannot figure out how.

    Any help would be appreciated.
    I would solve for each variable in terms of x.

    x=x
    y=\pm\sqrt{16-x^2}
    z=5-x

    Let x=t and now you have the vector function

    \left\langle t,\pm\sqrt{16-t^2},5-t\right\rangle, -4\leq t\leq 4
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  3. #3
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    Thanks for trying.
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  4. #4
    Super Member redsoxfan325's Avatar
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    Trying? Is that not the right answer?
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  5. #5
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    Ah yes its in a different form. The form i was looking at had sin(x) which when converted would work out. Thank!
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  6. #6
    Super Member redsoxfan325's Avatar
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    Quote Originally Posted by snaes View Post
    Ah yes its in a different form. The form i was looking at had sin(x) which when converted would work out. Thank!
    It was probably in polar. Something like:

    \langle 4\cos\theta,4\sin\theta,5-4\cos\theta\rangle for 0\leq\theta<2\pi
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