Let $$\phi $$ be an arbitrary smooth real valued scalar function and $$\overrightarrow V $$ be an arbitrary smooth vector valued function in a three dimensional space. Which one of the following is an identity?

Curl of vector $$\,\,\overrightarrow F = {x^2}{z^2}\widehat i - 2x{y^2}z\widehat j + 2{y^2}{z^3}\widehat k\,\,$$ is

Divergence of the vector field $${x^2}z\widehat i + xy\widehat j - y{z^2}\widehat k\,\,$$ at $$(1, -1, 1)$$ is

For the spherical surface $${x^2} + {y^2} + {z^2} = 1,$$ the unit outward normal vector at the point $$\left( {{1 \over {\sqrt 2 }},{1 \over {\sqrt 2 }},0} \right)$$ is given by