a:4:{s:8:"template";s:10276:"<!DOCTYPE html>
<html lang="en-US">
<head>
<meta charset="utf-8"/>
<meta content="width=device-width, initial-scale=1" name="viewport"/>
<link href="http://gmpg.org/xfn/11" rel="profile"/>

<title>{{ keyword }}</title>

<style id="cleanwp-maincss-css" media="all" rel="stylesheet" type="text/css">

/* Reset
-------------------------------------------------------------- */
html,body,div,h1,h2,a,ul,li,footer,header,nav {
    border: 0;
    font-family: inherit;
    font-size: 100%;
    font-style: inherit;
    font-weight: inherit;
    margin: 0;
    outline: 0;
    padding: 0;
    vertical-align: baseline;
}

html {
    font-family: sans-serif;
    font-size: 62.5%;
    overflow-y: scroll;
    -webkit-text-size-adjust: 100%;
    -ms-text-size-adjust: 100%;
}

*,*:before,*:after {
    -webkit-box-sizing: border-box;
    -moz-box-sizing: border-box;
    box-sizing: border-box;
}

body {
    background: #fff;
    line-height: 1;
}

footer,header,nav {
    display: block;
}

ul {
    list-style: none;
}

a {
    background-color: transparent;
}

a:focus {
    outline: thin dotted;
}

a:hover,a:active {
    outline: 0;
}

button {
    color: inherit;
    font: inherit;
    margin: 0;
}

button {
    overflow: visible;
}

button {
    text-transform: none;
}

button {
    -webkit-appearance: button;
    cursor: pointer;
}

button::-moz-focus-inner {
    border: 0;
    padding: 0;
}

/* Typography & Elements
-------------------------------------------------------------- */
body,button {
    color: #161514;
    font-family: Lora,Arial,sans-serif;
    font-size: 14px;
    line-height: 1.6;
}

button {
    max-width: 100%;
}

body {
    background: #717171;
}

a {
    color: #C90000;
    text-decoration: none;
    outline: none;
}

a:hover {
    color: #111111;
    text-decoration: none;
}

a:focus {
    outline: none;
}

h1,h2 {
    clear: both;
    font-family: 'Raleway',Arial,sans-serif;
    font-weight: 700;
    line-height: 1;
    margin: .6em 0;
}

h1 {
    font-size: 36px;
}

h2 {
    font-size: 24px;
}

ul {
    margin: 0 0 1.5em 3em;
}

ul {
    list-style: disc;
}

/* Clearings & Accessibility
-------------------------------------------------------------- */
.clear {
    clear: both;
}

.clearfix:before,.clearfix:after {
    content: " ";
    display: table;
}

.clearfix:after {
    clear: both;
}

.screen-reader-text {
    clip: rect(1px,1px,1px,1px);
    position: absolute!important;
    height: 1px;
    width: 1px;
    overflow: hidden;
}

.screen-reader-text:focus {
    background-color: #f1f1f1;
    border-radius: 3px;
    box-shadow: 0 0 2px 2px rgba(0,0,0,0.6);
    clip: auto!important;
    color: #21759b;
    display: block;
    font-size: 14px;
    font-weight: 700;
    height: auto;
    left: 5px;
    line-height: normal;
    padding: 15px 23px 14px;
    text-decoration: none;
    top: 5px;
    width: auto;
    z-index: 100000;
}

/* Forms
-------------------------------------------------------------- */
button {
    font-size: 100%;
    margin: 0;
    vertical-align: baseline;
}

button {
    border: 1px solid;
    border-color: #ccc #ccc #bbb;
    border-radius: 3px;
    background: #e6e6e6;
    -webkit-box-shadow: inset 0 1px 0 rgba(255,255,255,0.5),inset 0 15px 17px rgba(255,255,255,0.5),inset 0 -5px 12px rgba(0,0,0,0.05);
    -moz-box-shadow: inset 0 1px 0 rgba(255,255,255,0.5),inset 0 15px 17px rgba(255,255,255,0.5),inset 0 -5px 12px rgba(0,0,0,0.05);
    box-shadow: inset 0 1px 0 rgba(255,255,255,0.5),inset 0 15px 17px rgba(255,255,255,0.5),inset 0 -5px 12px rgba(0,0,0,0.05);
    color: rgba(0,0,0,.8);
    cursor: pointer;
    -webkit-appearance: button;
    font-size: 12px;
    line-height: 1;
    padding: .6em 1em .4em;
    text-shadow: 0 1px 0 rgba(255,255,255,0.8);
}

button:hover {
    border-color: #ccc #bbb #aaa;
    -webkit-box-shadow: inset 0 1px 0 rgba(255,255,255,0.8),inset 0 15px 17px rgba(255,255,255,0.8),inset 0 -5px 12px rgba(0,0,0,0.02);
    -moz-box-shadow: inset 0 1px 0 rgba(255,255,255,0.8),inset 0 15px 17px rgba(255,255,255,0.8),inset 0 -5px 12px rgba(0,0,0,0.02);
    box-shadow: inset 0 1px 0 rgba(255,255,255,0.8),inset 0 15px 17px rgba(255,255,255,0.8),inset 0 -5px 12px rgba(0,0,0,0.02);
}

button:focus,button:active {
    border-color: #aaa #bbb #bbb;
    -webkit-box-shadow: inset 0 -1px 0 rgba(255,255,255,0.5),inset 0 2px 5px rgba(0,0,0,0.15);
    -moz-box-shadow: inset 0 -1px 0 rgba(255,255,255,0.5),inset 0 2px 5px rgba(0,0,0,0.15);
    box-shadow: inset 0 -1px 0 rgba(255,255,255,0.5),inset 0 2px 5px rgba(0,0,0,0.15);
}

/* Layout
-------------------------------------------------------------- */
#wrapper {
    margin: 0 auto;
    position: relative;
}

#content {
    padding: 15px;
    width: 1030px;
    margin: 0 auto;
    background: #faf9f5;
    border-bottom: 1px solid #ddd;
}

/* Header
-------------------------------------------------------------- */
#masthead {
    background: #faf9f5;
    margin: 10px auto 0;
    padding: 10px 15px 10px 15px;
    width: 1030px;
}

#site-top {
    margin: 0;
    position: relative;
    overflow: hidden;
}

#blogname {
    margin: 0 0 10px 0;
    padding: 0;
    overflow: hidden;
}

.site-title {
    margin: 0 0 10px 0;
    text-align: center;
    font-size: 36px;
    font-weight: bold;
    color: #000000;
}

.site-title a {
    display: block;
    color: #000000;
}

.site-description {
    margin: 0 0 0 0;
    text-align: center;
    font-size: 18px;
    font-weight: bold;
    color: #000000;
}

.header-social-icons {
    font-family: Lora;
    font-size: 20px;
    padding: 10px 0 10px;
    text-align: center;
    line-height: 1;
}

/* Menu
-------------------------------------------------------------- */
.main-navigation {
    background-color: #777;
    display: block;
    padding: 0 10px;
    font-family: 'Raleway';
}

.main-navigation ul {
    list-style: none;
    margin: 0;
}

.main-navigation li {
    float: left;
    padding: 0;
    position: relative;
}

.main-navigation a {
    color: #fff;
    display: block;
    font-size: 13px;
    font-weight: bold;
    text-decoration: none;
    text-transform: uppercase;
    -webkit-transition: all .2s ease;
    transition: all .2s ease;
    padding: 10px;
}

.main-navigation a:hover {
    color: #ccc;
}

.menu-toggle {
    cursor: pointer;
    display: none;
}

@media screen and (max-width: 1049px) {
.menu-toggle {
    font-family: 'Raleway';
    font-weight: bold;
    background: none;
    border: none;
    -webkit-border-radius: 0;
    -moz-border-radius: 0;
    border-radius: 0;
    -webkit-box-shadow: none!important;
    -moz-box-shadow: none!important;
    box-shadow: none!important;
    color: #fff;
    display: block;
    font-size: 16px;
    margin: 0 auto;
    padding: 10px;
    text-align: center;
    text-shadow: none;
    text-transform: uppercase;
    width: 100%;
}

.menu-toggle:before {
    display: inline-block;
    font-family: FontAwesome;
    font-size: 16px;
    font-weight: normal;
    line-height: 1;
    vertical-align: text-bottom;
    -webkit-font-smoothing: antialiased;
    content: "\f0c9";
    margin-right: 12px;
    position: relative;
    top: -2px;
}

.menu-toggle {
    display: block;
}

.main-navigation {
    color: #fff;
    padding-right: 1em;
    padding-left: 1em;
}

.main-navigation ul {
    display: none;
}

.main-navigation ul a {
    font-size: 16px;
    text-transform: uppercase;
}

.main-navigation ul li {
    border-top: 0px dotted #5d5c5c;
    float: none;
    padding: 0;
}

.main-navigation ul li:first-child {
    border-top: 0;
}
}


.site-footer {
    width: 1030px;
    margin: 0 auto;
    padding: 20px 0 20px 0;
    background: #ddd;
    font-size: 90%;
}

.site-footer a:link,.site-footer a:visited {
}

.site-footer a:hover {
}

.site-info {
    text-align: center;
    line-height: 16px;
}


@media only screen and (max-width: 1049px) {
#content {
    width: 100%;
}

#masthead {
    width: 100%;
    padding: 10px 0 10px 0;
}

.site-title {
    padding-left: 10px;
    padding-right: 10px;
}

.site-description {
    padding-left: 10px;
    padding-right: 10px;
}

.site-footer {
    width: 100%;
}

.site-info {
    width: 100%;
}
}</style>
<style id="font-awesome-css" media="all" rel="stylesheet" type="text/css">/*!
 *  Font Awesome 4.5.0 by @davegandy - http://fontawesome.io - @fontawesome
 *  License - http://fontawesome.io/license (Font: SIL OFL 1.1, CSS: MIT License)
 */@font-face{font-family:'FontAwesome';src:url() format('embedded-opentype'),url(),url(),url(),url();font-weight:normal;font-style:normal}
</style>
<link href="//fonts.googleapis.com/css?family=Lora:400,700,400italic,700italic|Raleway:700,900,400,300&amp;subset=latin,latin-ext" id="cleanwp-webfont-css" media="all" rel="stylesheet" type="text/css"/>


<style type="text/css">
                                                                           		.entry-title a:hover {color: #444444}
                                                                                                                                                      															.entry-read-more {display: none;}
			</style>
<style id="custom-background-css" type="text/css">
body.custom-background { background-color: #777777; }
</style>
</head>
<body class="custom-background">
<div id="wrapper">
<a class="skip-link screen-reader-text" href="#">Skip to content</a>
<header class="site-header" id="masthead" role="banner">
<div id="site-top">
<div id="blogname">
<div class="site-branding">
<h1 class="site-title"><a href="#" rel="home">{{ keyword }}</a></h1>
<h2 class="site-description">The Internet It Just Gives and Gives and Gives.</h2>
</div>
</div>
<div class="header-social-icons">
</div>
</div>
<nav class="main-navigation clearfix" id="site-navigation" role="navigation">
<button aria-controls="primary-menu" aria-expanded="false" class="menu-toggle">Menu</button>
<div class="menu" id="primary-menu"><ul><li><a href="#">Home</a></li></ul></div>
</nav>
</header>
<div class="site-content" id="content">

{{ text }}

<div class="clear"></div>
</div>
</div>
<footer class="site-footer" id="colophon" role="contentinfo">
<div class="site-info">
  Copyright  2017 {{ keyword }} | <a href="#">Design by ThemesDNA.com</a>
</div>
<div class="clear"></div>
</footer>

</body>
</html>";s:4:"text";s:3021:"Product of three vectors. Vector calculus Up: Vectors Previous: The scalar triple product The vector triple product For three vectors , , and , the vector triple product is defined . The scalar triple product of the vectors a, b, and c: The volume of the parallelepiped determined by the vectors a, b, and c is the magnitude of their scalar triple product. Revision of vector algebra, scalar product, vector product 2. Triple products, multiple products, ... Another example 2.22 If $a$, $b$, $c$ are three vectors, then show that the vector triple product $(a \times b) \times c$ = $(c .a)b - (c . One such product is called the triple scalar product. The vector triple product of the vectors a, b, and c: Note that the result for the length of the cross product leads directly to the fact that two vectors are parallel if and only if their In this lesson, we explore this unique combination of vectors. Index Notation January 10, 2013 One of the hurdles to learning general relativity is the use of vector indices as a calculational tool. ... (for example to B, C, A) ... changes sign if you just reverse the vectors in the cross product. ... nal product of the rst vector triple product will be ... of all the tips of the vector A(t)) is a circle. b)a$ Proof of Vector Triple Product: 5.6 Vector Triple Products. ... For example, in our A triple scalar product is a unique combination of vectors. Vector Triple Product Proof Apr 27, 2007 #1 ... For example the scalar product [itex]u*v[/itex] ... Vector Triple Product Date; Vector triple product problem: In this presentation we shall review the properties related to vector triple products and solve some example problems. Lectures on Vector Calculus Paul Renteln Department of Physics California State University San Bernardino, CA 92407 March, 2009; Revised March, 2011 ... Scalar triple product of vectors (vector product) ... Scalar triple product examples. Example 1. Eighth Vector Mechanics for Engineers: Statics ...  Make sure you know how to solve HW problems and sample problems. Today's lecture was about Scalar Triple Products and Vector Triple Products.  Scalar Triple Product Formula. Vector Algebra and Calculus 1. I Triple product and volumes. Vector calculus Up: Vectors Previous: The scalar triple product The vector triple product For three vectors , , and , the vector triple product is defined . In vector algebra, a branch of mathematics, the triple product is a product of three 3-dimensional vectors, usually Euclidean vectors. So, (b x c) = ... Vector Addition Problems Organizing the Vector Products ... Mixed Triple Product of Three Vectors ... To understand the vector triple product better, ... Scalar Triple Product Examples; To evaluate this vector triple product, let us first evaluate the vector product inside the parenthesis. Scalar triple product. In this presentation we shall review the properties related to vector triple products and solve some example problems. Example Find the vector projection of a = h1,2ionto b = h4,1i. ";s:7:"keyword";s:38:"vector triple product example problems";s:7:"expired";i:-1;}