1.NounThe coefficient of k in the three-dimensional curl of a two-dimensional vector field."Since the curl of the vector field
F
→
=
(
x
y
,
x
y
,
0
)
{\displaystyle {\vec {F}}=(xy,xy,0)}
is the vector field
∇
→
×
F
→
=
(
0
,
0
,
y
−
x
)
{\displaystyle {\vec {\nabla }}\times {\vec {F}}=(0,0,y-x)}
, the scalar curl of the vector field
G
→
=
(
x
y
,
x
y
)
{\displaystyle {\vec {G}}=(xy,xy)}
is the scalar field
y
−
x
{\displaystyle y-x\;}
."