Vector Calculus Gradient

 $\overrightarrow{\ a\ }\ and\ \overrightarrow{\ b\ }\ are\ two\ non\ zero\ vectors\ then\ \left(\overrightarrow{\ a\ }\ \times\overrightarrow{\ b\ }\ \right)\ is\$  

 $i\times\left(\overrightarrow{\ a\ }\times i\right)+j\times\left(\overrightarrow{\ a\ }\times j\right)+k\times\left(\overrightarrow{\ a\ }\times k\right)=$  

The magnitude of vector  $\cos\theta\ i+\sin\theta\ j+k$  is

 $\nabla.\overrightarrow{\ r\ \ }\ =$ ,  or  div $\overrightarrow{\ r\ }$  =

 $\nabla^2\psi\left(x,y,z\right)=0,\$  the function  $\psi$  is

 $r=\left|\overrightarrow{\ r\ }\right|,\overrightarrow{\ r\ }=xi+yj+zk,\ then\ \Delta r=$  

 $\int_A^B\overrightarrow{f\ }.d\ \overrightarrow{r\ }$  is,

 $x=3t^2,\ y=t^2-2t,\ z=t^3$  ,A particle moves along the given above curves. the magnitude of velocity at t=1, is

 $\nabla\cdot\left(\nabla\times\overrightarrow{F}\right)$  
What will this operation result in?

 $\nabla\times\left(\nabla\cdot\overrightarrow{F}\right)$  
What will this operation result in?