Let F⃗(x,y,z)=(0,xz,xy)\vec{F}(x,y,z) = (0, xz, xy)F(x,y,z)=(0,xz,xy). Compute the curl ∇×F⃗\nabla \times \vec{F}∇×F at the point (1,1,0)(1,1,0)(1,1,0).
∇×F⃗(1,1,0)=(−1,−1,1)\nabla \times \vec{F}(1,1,0) = (-1, -1, 1)∇×F(1,1,0)=(−1,−1,1)
∇×F⃗(1,1,0)=(0,−1,0)\nabla \times \vec{F}(1,1,0) = (0, -1, 0)∇×F(1,1,0)=(0,−1,0)
∇×F⃗(1,1,0)=(1,−1,1)\nabla \times \vec{F}(1,1,0) = (1, -1, 1)∇×F(1,1,0)=(1,−1,1)
∇×F⃗(1,1,0)=(−1,1,1)\nabla \times \vec{F}(1,1,0) = (-1, 1, 1)∇×F(1,1,0)=(−1,1,1)