[Solution] Use Stokes' Theorem to compute ∫_C F • d \vecs where F(x, y, z)=y^2 \veci+z^2 \vecj+x \veck and the curve C is the triangle in 3 -space
Question: Use Stokes' Theorem to compute \(\int_{C} \vec{F} \cdot d \vec{s}\) where \(\vec{F}(x, y, z)=y^{2} \vec{i}+z^{2} \vec{j}+x \vec{k}\) and the curve \(C\) is the triangle in 3 -space with vertices at \((1,0,0),(0,2,0)\), and \((0,0,3)\).
Hints:
- For the surface \(S\) needed in Stokes' Theorem, use the part of the plane \(x+\frac{y}{2}+\frac{z}{3}=1\) that lies in the first octant.
- That plane can be written parametrically as \(\Phi(x, y)=\left\langle x, y, 3-3 x-\frac{3}{2} y\right\rangle\).
- Make sure you have the upward pointing normal!
Deliverable: Word Document 
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