91Ó°ÊÓ

Find the work done by the force field \(\mathbf{F}\) on a particle moving along the given path. \(\mathbf{F}(x, y)=2 x \mathbf{i}+y \mathbf{j}\) \(C:\) counterclockwise around the triangle with vertices \((0,0),\) \((1,0),\) and (1,1)

Find the divergence of the vector field \(\mathrm{F}\). \(\mathbf{F}(x, y, z)=6 x^{2} \mathbf{i}-x y^{2} \mathbf{j}\)

Find a vector-valued function for the hyperboloid \(x^{2}+y^{2}-z^{2}=1\) and determine the tangent plane at \((1,0,0) .\)