Sketch the vector field F(x, y) = (-x − y, x - y) at the points (x, y) where x, y = {−1,0,1}.
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- Sketch the vector field F(x,y)=1/2xi-1/2yj at points (-1,1), (-1,0),(-1,1),(0,-1),(0,0),(0,1),(1,-1),(1,0),(1,1)What is the flux of the vector field F(x, y, z) = [9y, 2xy, 4yz + 234xy] through the unit cube [0,1] x [0,1] x [0,1].Find the divergence of the vector field F→(x,y,z)=xyzi→−yzj→+xzk→at the point (8,3,2) . Enter the exact answer. divF→(8,3,2)=
- Find the work W done by the vector field ⟨2x+yx,x2+4⟩ on a particle moving along the boundary of the rectangle 0≤x≤2,0≤y≤5 in the counterclockwise direction.Show that Gauss's Theorem holds for the vector field F(x, y)=(xy2, -yx2) in a side square 3.Show that the vector field F(x,y,z)=(−5ycos(9x),9xsin(−5y),0) is not a gradient vector field by computing its curl. How does this show what you intended? curl(F)=∇×F=?
