\(\newcommand{\del}[2]{\frac{\partial #1}{\partial #2}} \def\proj{\qopname\relax o{proj}} \def\grad{\qopname\relax o{grad}} \def\curl{\text{curl }\ } \def\div{\qopname\relax o{div}} \def\comp{\qopname\relax o{comp}} \newcommand{\R}{\mathbb{R}} \definecolor{purple}{rgb}{0.5,0,1.0} \definecolor{cyan}{rgb}{0, 1, 1} \definecolor{hotpink}{rgb}{1, 0, 0.5} \definecolor{skyblue}{rgb}{0, 0.5, 1} \newcommand{\lt}{<} \newcommand{\gt}{>} \newcommand{\amp}{&} \)