\(\newcommand{\R}{\mathbb{R}} \newcommand{\va}{\mathbf{a}} \newcommand{\vb}{\mathbf{b}} \newcommand{\vc}{\mathbf{c}} \newcommand{\vC}{\mathbf{C}} \newcommand{\vd}{\mathbf{d}} \newcommand{\ve}{\mathbf{e}} \newcommand{\vi}{\mathbf{i}} \newcommand{\vj}{\mathbf{j}} \newcommand{\vk}{\mathbf{k}} \newcommand{\vn}{\mathbf{n}} \newcommand{\vm}{\mathbf{m}} \newcommand{\vr}{\mathbf{r}} \newcommand{\vs}{\mathbf{s}} \newcommand{\vu}{\mathbf{u}} \newcommand{\vv}{\mathbf{v}} \newcommand{\vw}{\mathbf{w}} \newcommand{\vx}{\mathbf{x}} \newcommand{\vy}{\mathbf{y}} \newcommand{\vz}{\mathbf{z}} \newcommand{\vzero}{\mathbf{0}} \newcommand{\vF}{\mathbf{F}} \newcommand{\vG}{\mathbf{G}} \newcommand{\vH}{\mathbf{H}} \newcommand{\vR}{\mathbf{R}} \newcommand{\vT}{\mathbf{T}} \newcommand{\vN}{\mathbf{N}} \newcommand{\vL}{\mathbf{L}} \newcommand{\vB}{\mathbf{B}} \newcommand{\vS}{\mathbf{S}} \newcommand{\proj}{\text{proj}} \newcommand{\comp}{\text{comp}} \newcommand{\nin}{} \newcommand{\vecmag}[1]{|#1|} \newcommand{\grad}{\nabla} \DeclareMathOperator{\curl}{curl} \DeclareMathOperator{\divg}{div} \newcommand{\lt}{<} \newcommand{\gt}{>} \newcommand{\amp}{&} \)