The value of the line integral $$\,\,\oint\limits_C {\overrightarrow F .\overrightarrow r ds,\,\,\,} $$ where $$C$$ is a circle of radius $${4 \over {\sqrt \pi }}\,\,$$ units is ________.

Here, $$\,\,\overrightarrow F x,y = y\widehat i + 2x\widehat j\,\,$$ and $$\,\overrightarrow r $$ is the UNIT tangent vector on the curve $$C$$ at an arc length s from a reference point on the curve. $$\widehat i$$ and $$\widehat j$$ are the basis vectors in the $$X-Y$$ Cartesian reference. In evaluating the line integral, the curve has to be traversed in the counter-clockwise direction.

The velocity field on an incompressible flow is given by
$$V = \left( {{a_1}x + {a_2}y + {a_3}z} \right)i + \left( {{b_1}x + {b_2}y + {b_3}z} \right)j\,$$ $$ + \left( {{c_1}x + {c_2}y + {c_3}z} \right)k,\,\,$$
where $${{a_1} = 2}$$ and $${{c_3} = - 4.}$$ The value of $${{b_2}}$$ is ________.

The surface integral $$\,\,\int {\int\limits_s {{1 \over \pi }} } \left( {9xi - 3yj} \right).n\,dS\,\,$$ over the sphere given by $${x^2} + {y^2} + {z^2} = 9\,\,$$ is __________.

The value of $$\int\limits_C {\left[ {\left( {3x - 8{y^2}} \right)dx + \left( {4y - 6xy} \right)dy} \right],\,\,} $$ (where $$C$$ is the region bounded by $$x=0,$$ $$y=0$$ and $$x+y=1$$) is ________.