Find the curl of the vector field F(x,y,z) = (z + 𝑥^2 y) i + (xyz) j + (x + 𝑦^2 𝑧) 𝒌 at the point P(1,1,1)?

Answer 1

It's just ∇×F:
|i j k|
|∂/∂x ∂/∂y ∂/∂z|
|z+x^2y xyz x+y^2z|
= (2yz - xy)i + (1-1)j + (yz-1)k