Question

1)Use Stokes' Theorem to find the circulation of F⃗ =2yi⃗ +2zj⃗ +2xk⃗ around the triangle obtained by tracing out the path (2,0,0) to (2,0,2), to (2,5,2) back to (2,0,0).

Circulation = ∫CF⃗ ⋅dr⃗ =

Answer 1

compute the curl of the field,
and use the area of the triangle as S,

Answer 2

Stokes' Theorem
\[\oint_C\vec {\mathbf F}\cdot\mathrm d\vec {\mathbf r}=\iint_S(\nabla\times\vec {\mathbf F})\cdot\mathrm d\vec {\mathbf S}\]

Answer 3

the curl is <-2,-2,-2> and F=<2y,2z,2x> how do i find the triangle area?