Check the Stokes' theorem for the function [tex]\vec v = y\hat z[/tex](adsbygoogle = window.adsbygoogle || []).push({});

Here it is over a tetrahedron.

Stokes' theorem suggests:

[tex]\int_s {(\nabla\times \vec v).d\vec a = \oint_p\vec v.d\vec r [/tex]

For the right hand side I computed the line integral from (a,0,0)--->(0,2a,0)--->(0,0,a)--->(a,0,0);

which comes out to be [tex]a^2[/tex] (matches with the solution given).

For the surface integral, one needs to obtain the expression for the area element[tex]d\vec a[/tex] of the plane given by the above points, which is where my problem lies. Can someone help me on this?

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# Homework Help: Stokes' theorem over a tetrahedron

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