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