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Author: Tinku Tara

Question-219374

Question Number 219374 by SdC355 last updated on 23/Apr/25 Commented by SdC355 last updated on 23/Apr/25 $$\overset{\rightarrow} {\boldsymbol{\mathcal{S}}}\left({u},{v}\right)=\begin{cases}{\left(\mathrm{2}+{v}\centerdot\mathrm{sin}\left({u}\right)\right)\mathrm{sin}\left(\mathrm{2}\pi{v}\right)}\\{{v}\centerdot\mathrm{cos}\left({u}\right)}\\{\left(\mathrm{2}+{v}\centerdot\mathrm{sin}\left({u}\right)\right)\mathrm{cos}\left(\mathrm{2}\pi{v}\right)+\left(\mathrm{2}{v}−\mathrm{2}\right)}\end{cases} \\ $$$${u}\in\left[−\pi,\pi\right]\:,\:{v}\in\left[\mathrm{0},\frac{\pi}{\mathrm{2}}\right] \\ $$$$\mathrm{and}\:\mathrm{vector}\:\mathrm{field}\:\overset{\rightarrow} {\boldsymbol{\mathrm{F}}}\left({x},{y},{z}\right)=−{x}\overset{\rightarrow} {\boldsymbol{\mathrm{e}}}_{\mathrm{1}} −{y}\overset{\rightarrow}…