<html><head><meta name="color-scheme" content="light dark"></head><body><pre style="word-wrap: break-word; white-space: pre-wrap;">\documentclass[a4paper,12pt]{article}
\usepackage{epsfig}
\newcommand{\dci}{\rlap{$\displaystyle\int\!\!\!\int_{B_{a,b,c}}$}
{\hspace{2.2pt}\bigcirc} \ \ }
\newcommand{\un}{\underline}
\begin{document}
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\begin{center}
\textbf{Vector Calculus}

\textit{\textbf{Grad, Div and Curl}}
\end{center}

\textbf{Question}


Calculate $\textbf{\textrm{div}F}$ and $\textbf{\textrm{curl}F}$ for
the vector field

$\un{F} = yz\un{i} + xz\un{j} + xy\un{k}$


\textbf{Answer}

\begin{eqnarray*}
\textrm{div}\un{F} &amp; = &amp; \frac{\partial}{\partial x}(
yz )+\frac{\partial}{\partial y}(
xz ) +\frac{\partial}{\partial z}(
xy ) = 0\\
\textrm{curl}\un{F} &amp; = &amp; \left | \begin{array}{ccc} \un{i} &amp; \un{j} &amp;
\un{k}\\ \frac{\partial}{\partial x} &amp; \frac{\partial}{\partial y} &amp;
\frac{\partial}{\partial z}\\
yz &amp; xz &amp; xy
\end{array}
\right |\\
&amp; = &amp; (x-x)\un{i} +(y-y)\un{j} +(z-z)\un{k} = \un{0}
\end{eqnarray*}

\end{document}
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