Example 2.2.3: Curl of a vector field

With $B_x=3y^{2}z$, $B_y=-xz$, $B_z=2z^3$, the three brackets of (2.2.8) are

The curl is a vector field. Notice that the term $2z^3{a}_z$ of $B$ does not contribute at all: a component that depends only on its own coordinate has no "side pushed harder than the other".