How to find the projection of a cylinder projected onto a plane?

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Say you are given the equations:



$x + y + z = 6$
and $x^2 + y^2 = 1$



You can easily find the plane and cylinder accordingly. But how do you find the projection of the cylinder onto that plane. The $x$ boundaries should be the radius of the circle.



I've been told you parametrise both equations and work from there, is that correct?



This is for evaluating Stokes' Theorem by the way.




calculus multivariable-calculus vector-analysis




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    Are you sure that you mean "projection"? The projection of the cylinder onto the plane is like the shadow of the cylinder. Do you mean intersection?
    – Kyle
    Jun 9 '14 at 13:25














up vote
2
down vote

favorite












Say you are given the equations:



$x + y + z = 6$
and $x^2 + y^2 = 1$



You can easily find the plane and cylinder accordingly. But how do you find the projection of the cylinder onto that plane. The $x$ boundaries should be the radius of the circle.



I've been told you parametrise both equations and work from there, is that correct?



This is for evaluating Stokes' Theorem by the way.




calculus multivariable-calculus vector-analysis




share|cite|improve this question
















  • 2




    Are you sure that you mean "projection"? The projection of the cylinder onto the plane is like the shadow of the cylinder. Do you mean intersection?
    – Kyle
    Jun 9 '14 at 13:25












up vote
2
down vote

favorite









up vote
2
down vote

favorite











Say you are given the equations:



$x + y + z = 6$
and $x^2 + y^2 = 1$



You can easily find the plane and cylinder accordingly. But how do you find the projection of the cylinder onto that plane. The $x$ boundaries should be the radius of the circle.



I've been told you parametrise both equations and work from there, is that correct?



This is for evaluating Stokes' Theorem by the way.




calculus multivariable-calculus vector-analysis




share|cite|improve this question












Say you are given the equations:



$x + y + z = 6$
and $x^2 + y^2 = 1$



You can easily find the plane and cylinder accordingly. But how do you find the projection of the cylinder onto that plane. The $x$ boundaries should be the radius of the circle.



I've been told you parametrise both equations and work from there, is that correct?



This is for evaluating Stokes' Theorem by the way.





calculus multivariable-calculus vector-analysis





share|cite|improve this question











share|cite|improve this question




share|cite|improve this question










asked Jun 9 '14 at 12:59









Dan

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  • 2




    Are you sure that you mean "projection"? The projection of the cylinder onto the plane is like the shadow of the cylinder. Do you mean intersection?
    – Kyle
    Jun 9 '14 at 13:25












  • 2




    Are you sure that you mean "projection"? The projection of the cylinder onto the plane is like the shadow of the cylinder. Do you mean intersection?
    – Kyle
    Jun 9 '14 at 13:25







2




2




Are you sure that you mean "projection"? The projection of the cylinder onto the plane is like the shadow of the cylinder. Do you mean intersection?
– Kyle
Jun 9 '14 at 13:25




Are you sure that you mean "projection"? The projection of the cylinder onto the plane is like the shadow of the cylinder. Do you mean intersection?
– Kyle
Jun 9 '14 at 13:25










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I would say that parametric equations intersection of the two surfaces may be necessary



$x = cos t, ,y = sin t, , z = 6-cos t-sin t;, t, epsilon , langle 0,2pirangle$






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    I would say that parametric equations intersection of the two surfaces may be necessary



    $x = cos t, ,y = sin t, , z = 6-cos t-sin t;, t, epsilon , langle 0,2pirangle$






    share|cite|improve this answer
























      up vote
      0
      down vote













      I would say that parametric equations intersection of the two surfaces may be necessary



      $x = cos t, ,y = sin t, , z = 6-cos t-sin t;, t, epsilon , langle 0,2pirangle$






      share|cite|improve this answer






















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        up vote
        0
        down vote









        I would say that parametric equations intersection of the two surfaces may be necessary



        $x = cos t, ,y = sin t, , z = 6-cos t-sin t;, t, epsilon , langle 0,2pirangle$






        share|cite|improve this answer












        I would say that parametric equations intersection of the two surfaces may be necessary



        $x = cos t, ,y = sin t, , z = 6-cos t-sin t;, t, epsilon , langle 0,2pirangle$







        share|cite|improve this answer












        share|cite|improve this answer



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        answered Jun 9 '14 at 13:20









        georg

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