Use Stokes' Theorem to find the circulation of F⃗ =6yi⃗ +4zj⃗ +3xk⃗ around the triangle obtained by tracing out the path (3,0,0) to (3,0,3), to (3,4,3) back to (3,0,0).

I've found the curl(F) = (-4,-3,-6) and the equation of the plane containing the triangle to be -12x=-36 (x=4). I also know that using the parameterization, I can find the normal vector to the surface by using a 3x3 matrix. I just need help parameterizing the triangle.

Question

Use Stokes' Theorem to find the circulation of F⃗ =6yi⃗ +4zj⃗ +3xk⃗  around the triangle obtained by tracing out the path (3,0,0) to (3,0,3), to (3,4,3) back to (3,0,0). 

I've found the curl(F) = (-4,-3,-6) and the equation of the plane containing the triangle to be -12x=-36 (x=4). I also know that using the parameterization, I can find the normal vector to the surface by using a 3x3 matrix. I just need help parameterizing the triangle.

hayhayz · Answer

Integral Curl f .n ds =the boundary line integral fdotdr

dan815 · Answer

your plane equation doesnt make sense

dan815 · Answer

cross the 2 vectors on your triangle to get the normal line

dan815 · Answer

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dan815 · Answer

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