13.5 number 9 (updated)

I do not know how to approach this at all.  Please give me some insight!  I
work the majority of the weekend, so an extension until Sunday would be
heaven-sent too.  If not, I'll do what I can before midnight.  Just
throwing that in there! ;-)

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First of all, the book talks about this in some detail. I recommend that everybody read it.  The *general* notion is that the curl measures both the amount and direction of circulation around an axis--for which counter-clockwise is positive--as well as the direction of the axis as a vector.  The important examples to keep in mind are the ones we worked in class last Friday: the vector fields

F=xi+yj+zk for which curl(F)=0

and the vector field F=yi-xj+0k, which looks like this:

for which curl(F)=-2k (and the negative is because the vector field is circulating clockwise around the z-axis).