Show that \(\operatorname{curl}(\mathbf{F})=\mathbf{0}\) if \(\mathbf{F}\) is radial, meaning that \(\mathbf{F}=f(ho)\langle x, y, zangle\) for some function \(f(ho)\), where \(ho=\sqrt{x^{2}+y^{2}+z^{2}}\). Hint: It is enough to show that one component of \(\operatorname{curl}(\mathbf{F})\) is zero, because it will then follow for the other two components by symmetry.