BacCabRule 2003-11-27 14:01:04 2003-12-01 02:22:27 Result cross product % this is the default PlanetMath preamble. as your knowledge % of TeX increases, you will probably want to edit this, but % it should be fine as is for beginners. % almost certainly you want these \usepackage{amssymb} \usepackage{amsmath} \usepackage{amsfonts} % used for TeXing text within eps files %\usepackage{psfrag} % need this for including graphics (\includegraphics) %\usepackage{graphicx} % for neatly defining theorems and propositions %\usepackage{amsthm} % making logically defined graphics %\usepackage{xypic} % there are many more packages, add them here as you need them % define commands here \newcommand{\sR}[0]{\mathbb{R}} \newcommand{\sC}[0]{\mathbb{C}} \newcommand{\sN}[0]{\mathbb{N}} \newcommand{\sZ}[0]{\mathbb{Z}} % The below lines should work as the command % \renewcommand{\bibname}{References} % without creating havoc when rendering an entry in % the page-image mode. \makeatletter \@ifundefined{bibname}{}{\renewcommand{\bibname}{References}} \makeatother \newcommand*{\norm}[1]{\lVert #1 \rVert} \newcommand*{\abs}[1]{| #1 |} The {\bf bac-cab rule} states that for vectors $\mathbf{A}$, $\mathbf{B}$, and $\mathbf{C}$ (that can be either real or complex) in $\sR^3$, we have $$ \mathbf{A}\times (\mathbf{B}\times \mathbf{C}) = \mathbf{B} (\mathbf{A}\cdot \mathbf{C}) - \mathbf{C} (\mathbf{A} \cdot \mathbf{B}).$$ Here $\times$ is the cross product, and $\cdot$ is the real inner product.