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Use stokes theorem to show that:

$$\int_c ydx + zdy +xdz = -\sqrt{3} \pi a^2$$

Where c is the suitably oriented intersection of the surfaces $x^2 + y^2 +z^2=a^2$ and the plane $x+y+z=0$.

user49541
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    Have you tried anything so far? – Javier Nov 15 '12 at 15:53
  • yeah the curl of F is $(-1,-1,-1)$ and i have dotted this with the normal to the sphere in spherical coordinates but i do not know how to get the parameter domain when the sphere is parameterised in spherical coordinates – user49541 Nov 15 '12 at 15:59
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    Don't understand why the question has 3 up-votes... does it show research effort and an attempt at answering the question?? – Epictetus Nov 15 '12 at 16:09

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