Exercise 1198Calculus › Multivariable calculus › Vector calculusL1Added 3 Nov 2026

The curl

#curl#vector field#rotation

Statement

Compute $\nabla\times\vec F$ for $\vec F=(yz,\,xz,\,xy)$ .

Hint

$\nabla\times\vec F=(R_y-Q_z,\,P_z-R_x,\,Q_x-P_y)$ .

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Compute.
- $R_y-Q_z=x-x=0$
- $P_z-R_x=y-y=0$
- $Q_x-P_y=z-z=0$

Conclusion. $\nabla\times\vec F=\vec0$ : the field is irrotational. It is actually conservative with potential $\phi=xyz$ .