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in Vectors by (15 points)
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Show that vector F = yzi + zxj + xyk is irrotational.

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\(\vec F=yz\hat i+zx\hat j+xy\hat k\)

\(\vec ▽\times\vec F\) = \(\begin{vmatrix}\hat i&\hat j&\hat k\\ \frac{\partial}{\partial x}&\frac{\partial}{\partial y}&\frac{\partial}{\partial z}\\yz&zx&xy\end {vmatrix}\)

 = \(\hat i(x-x)-\hat j(y-y)+\hat k(z-z)\)

 = \(0\hat i+0\hat j+0\hat k\)

 = \(\vec 0\)

∴ vector \(\vec F\) is an irrotational vector.

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