What will be the 4th axis of a 3d curl?

[malfoy23111995]

Suppose we have do a curl of two 2-d vectors... we get the 3rd axis about which it is rotating. But when we do the curl of two 3-d vectors.. we get a answer like x-y plane is rotating wrt z axis, y-z plane rotating wrt to x-axis and similarly x-z plane rotating wrt to y axis.
My question is, can't we find out the 4th dimension with respect to which all the x-y-z volume is rotating?

 

[Nugatory]

Your "two 2-d vectors" and "two 3-d vectors" are actually the exact same thing. The two "3d vectors" lie in a common 2d plane, just as do you "2d" vectors, and then the curl is perpendicular to that plane, in the third dimension.