<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{\pa}{\partial}
\newcommand{\ds}{\displaystyle}
\newcommand{\un}{\underline}
\begin{document}
\parindent=0pt

\begin{center}
\textbf{Vector Fields}

\textit{\textbf{Conservative Fields}}
\end{center}

\textbf{Question}

Calculate $\nabla \ln |\un{r}|$, with $\un{r} = x\un{i} + y\un{j} +
z\un{k}$.


\textbf{Answer}

\begin{eqnarray*}
\frac{\pa}{\pa x} \ln |\un{r}| &amp; = &amp; \frac{1}{|\un{r}|} \frac{\un{r}
\bullet \frac{\pa \un{r}}{\pa x}}{|\un{r}|} = \frac{x}{|\un{r}|^2}\\
\nabla \ln |\un{r}| &amp; = &amp; \frac{x\un{i} +y\un{j}
+z\un{k}}{|\un{r}|^2}\\
&amp; = &amp; \frac{\un{r}}{|\un{r}|^2}
\end{eqnarray*}


\end{document}




















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