Determine whether the curl of each vector field F at the ori

Determine whether the curl of each vector field F at the origin (in red) is 0 or points in the same direction as plusminus i, plusminus j, or plusminus k.

Solution

top left: the vector field looks like (0,y,0) , giving a curl of (0,0,0) .so answer is <0,0,0>
top right: the field looks like (z,0,0), giving a curl of (0,1,0) so answer is  j = <0,1,0>
bottom left: the diagram is unclear. it might be (y, -x, 0) giving a curl of (0,0, -2) .so answer is  -k = <0,0,-1>.
bottom right, the field is (x,y,z) giving a curl of (0,0,0 ) so answer is  <0,0,0>