\(\vec F=yz\hat i+zx\hat j+xy\hat k\)
\(\vec ▽\times\vec F\) = \(\begin{vmatrix}\hat i&\hat j&\hat k\\ \frac{\partial}{\partial x}&\frac{\partial}{\partial y}&\frac{\partial}{\partial z}\\yz&zx&xy\end {vmatrix}\)
= \(\hat i(x-x)-\hat j(y-y)+\hat k(z-z)\)
= \(0\hat i+0\hat j+0\hat k\)
= \(\vec 0\)
∴ vector \(\vec F\) is an irrotational vector.