Curl, Calc 3 Question

I do not know how to calculate 2D curls.

Question: Find the curl of [2x-3y , -3x+4y-8]

How is the procedure different from that of a 3D curl?

Please and thank you.

I may be a bit rusty but lets give it a try..

del x F = curl of F

where F is a vector field..

|...i.........j..........k|
|d/dx..d/dy....d/dz|
|2x-3y.-3x+4y-8..0|

we can see the i component will be 0

this is because d/dz of a function of x and y = 0

also d0/dy = 0

so the i component must be 0

same with the j component must be 0

because d0/dx = 0
and d/dz of a function of x and y is also 0

this means there is only one component..

k(d(-3x + 4y -8)/dx - d(2x -3y)/dy)

this is basically what is called greens theorem I think...

k(-3 - (-3))
= k(0)

in this case the answer curl of the question given is 0

all I did was a normal 3 dimensional curl with the z component added as 0

It isn't. Just do it and get curl([2x-3]i + [-3x+4y-8]j) = 0

Check my algebra....