The directional derivative of the function $f$ given below at the point $(1,0)$ in the direction of $\frac{1}{2}(\hat{i}+\sqrt{3} \hat{j})$ is _______ (Rounded off to 1 decimal place).

$$ f(x, y)=x^2+x y^2 $$

Consider two vectors

$\rm \vec a = 5 i + 7 j + 2 k $

$\rm \vec b = 3i - j + 6k$

Magnitude of the component of $\vec a$ orthogonal to $\vec b$ in the plane containing the vectors $\vec a$ and $\vec{\bar b}$ is ______ (round off to 2 decimal places).

The surface integral $$\int {\int\limits_s {F.ndS} } $$ over the surface $$S$$ of the sphere $${x^2} + {y^2} + {z^2} = 9,$$ where $$\,F = \left( {x + y} \right){\rm I} + \left( {x + z} \right)j + \left( {y + z} \right)k\,\,$$ and $$n$$ is the unit outward surface normal, yields ___________.

For the vector $$\overrightarrow V = 2yz\widehat i + 3xz\widehat j + 4xy\widehat k,$$ the value of $$\,\nabla .\left( {\nabla \times \overrightarrow \nabla } \right)\,\,$$ is ______________.