Let $$\,\,\nabla .\left( {fV} \right) = {x^2}y + {y^2}z + {z^2}x,\,\,$$ where $$f$$ and $$V$$ are scalar and vector fields respectively. If $$V=yi+zj+xk,$$ then $$\,V.\left( {\nabla f} \right)$$ is

The line integral of function $$F=yzi,$$ in the counterclockwise direction, along the circle $${x^2} + {y^2} = 1$$ at $$z=1$$ is

The two vectors $$\left[ {\matrix{ {1,} & {1,} & {1} \cr } } \right]$$ and $$\left[ {\matrix{ {1,} & {a,} & {{a^2}} \cr } } \right]$$ where $$a = {{ - 1} \over 2} + j{{\sqrt 3 } \over 2}$$ are

Divergence of the $$3$$ $$-$$ dimensional radial vector field $$\overrightarrow r $$ is