VectorIdentities 2006-07-20 18:59:21 2006-07-20 18:59:21 Definition Vector Identities % 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 It is difficult to get anywhere in physics without a firm understanding of vectors and their common operations. Here, we will give vector identities as a reference. Basic terminology to keep straight. \begin{table}[t] \begin{center} \begin{tabular}{cc} \\ [.3ex] \hline \\ [.3ex] {\bf Operation} & {\bf Symbol} \\ [0.5ex] %heading \hline \\ [.3ex] Gradient & $\nabla f$ \\ Laplacian & $\nabla^2$ \\ Divergence & $\nabla \cdot$ \\ Curl & $\nabla \times$ \\ \hline \end{tabular} \end{center} \end{table} {\bf Vector Triple Product, aka. BAC CAB} $ \mathbf{A} \times \left ( \mathbf{B} \times \mathbf{C} \right ) = \mathbf{B} \left( \mathbf{A} \cdot \mathbf{C} \right ) - \mathbf{C} \left ( \mathbf{A} \cdot \mathbf{B} \right) $ {\bf Scalar Triple Product} $ \mathbf{A} \cdot \left ( \mathbf{B} \times \mathbf{C} \right ) = \mathbf{B} \cdot \left ( \mathbf{C} \times \mathbf{A} \right ) = \mathbf{C} \cdot \left ( \mathbf{A} \times \mathbf{B} \right ) $