a:4:{s:8:"template";s:8126:"<!DOCTYPE html>
<html lang="en-US">

<head>
<meta charset="utf-8"/>
<meta content="width=device-width" name="viewport"/>
<title>{{ keyword }}</title>
<link href="http://gmpg.org/xfn/11" rel="profile"/>


<link href="http://fonts.googleapis.com/css?family=Open+Sans:400italic,700italic,400,700&amp;subset=latin,latin-ext" id="twentytwelve-fonts-css" media="all" rel="stylesheet" type="text/css"/>
<style id="twentytwelve-style-css" media="all" rel="stylesheet" type="text/css">/*



/* =Reset
-------------------------------------------------------------- */

html, body, div, h1, h2, h3, a, ul, li, footer, header, hgroup, nav {
	margin: 0;
	padding: 0;
	border: 0;
	font-size: 100%;
	vertical-align: baseline;
}
body {
	line-height: 1;
}
ul {
	list-style: none;
}
h1,
h2,
h3 {
	clear: both;
}
html {
	overflow-y: scroll;
	font-size: 100%;
	-webkit-text-size-adjust: 100%;
	-ms-text-size-adjust: 100%;
}
a:focus {
	outline: thin dotted;
}
footer,
header,
hgroup,
nav {
	display: block;
}

/* Clearing floats */
.wrapper:after {
	clear: both;
}
.wrapper:before,
.wrapper:after {
	display: table;
	content: "";
}


.menu-toggle {
	padding: 6px 10px;
	padding: 0.428571429rem 0.714285714rem;
	font-size: 11px;
	font-size: 0.785714286rem;
	line-height: 1.428571429;
	font-weight: normal;
	color: #7c7c7c;
	background-color: #e6e6e6;
	background-repeat: repeat-x;
	background-image: -moz-linear-gradient(top, #f4f4f4, #e6e6e6);
	background-image: -ms-linear-gradient(top, #f4f4f4, #e6e6e6);
	background-image: -webkit-linear-gradient(top, #f4f4f4, #e6e6e6);
	background-image: -o-linear-gradient(top, #f4f4f4, #e6e6e6);
	background-image: linear-gradient(top, #f4f4f4, #e6e6e6);
	border: 1px solid #d2d2d2;
	border-radius: 3px;
	box-shadow: 0 1px 2px rgba(64, 64, 64, 0.1);
}
.menu-toggle {
	cursor: pointer;
}
.menu-toggle:hover {
	color: #5e5e5e;
	background-color: #ebebeb;
	background-repeat: repeat-x;
	background-image: -moz-linear-gradient(top, #f9f9f9, #ebebeb);
	background-image: -ms-linear-gradient(top, #f9f9f9, #ebebeb);
	background-image: -webkit-linear-gradient(top, #f9f9f9, #ebebeb);
	background-image: -o-linear-gradient(top, #f9f9f9, #ebebeb);
	background-image: linear-gradient(top, #f9f9f9, #ebebeb);
}
.menu-toggle:active {
	color: #757575;
	background-color: #e1e1e1;
	background-repeat: repeat-x;
	background-image: -moz-linear-gradient(top, #ebebeb, #e1e1e1);
	background-image: -ms-linear-gradient(top, #ebebeb, #e1e1e1);
	background-image: -webkit-linear-gradient(top, #ebebeb, #e1e1e1);
	background-image: -o-linear-gradient(top, #ebebeb, #e1e1e1);
	background-image: linear-gradient(top, #ebebeb, #e1e1e1);
	box-shadow: inset 0 0 8px 2px #c6c6c6, 0 1px 0 0 #f4f4f4;
	border: none;
}


/* Body, links, basics */
html {
	font-size: 87.5%;
}
body {
	font-size: 14px;
	font-size: 1rem;
	font-family: Helvetica, Arial, sans-serif;
	text-rendering: optimizeLegibility;
	color: #444;
}
body.custom-font-enabled {
	font-family: "Open Sans", Helvetica, Arial, sans-serif;
}
a {
	outline: none;
	color: #21759b;
}
a:hover {
	color: #0f3647;
}

/* Assistive text */
.assistive-text {
	position: absolute !important;
	clip: rect(1px, 1px, 1px, 1px);
}
.main-navigation .assistive-text:hover,
.main-navigation .assistive-text:active,
.main-navigation .assistive-text:focus {
	background: #fff;
	border: 2px solid #333;
	border-radius: 3px;
	clip: auto !important;
	color: #000;
	display: block;
	font-size: 12px;
	padding: 12px;
	position: absolute;
	top: 5px;
	left: 5px;
	z-index: 100000; /* Above WP toolbar */
}

/* Page structure */
.site {
	padding: 0 24px;
	padding: 0 1.714285714rem;
	background-color: #fff;
}

/* Header */
.site-header {
	padding: 24px 0;
	padding: 1.714285714rem 0;
}
.site-header h1,
.site-header h2 {
	text-align: center;
}
.site-header h1 a {
	color: #515151;
	display: inline-block;
	text-decoration: none;
}
.site-header h1 a:hover {
	color: #21759b;
}
.site-header h1 {
	font-size: 24px;
	font-size: 1.714285714rem;
	line-height: 1.285714286;
	margin-bottom: 14px;
	margin-bottom: 1rem;
}
.site-header h2 {
	font-weight: normal;
	font-size: 13px;
	font-size: 0.928571429rem;
	line-height: 1.846153846;
	color: #757575;
}

/* Navigation Menu */
.main-navigation {
	margin-top: 24px;
	margin-top: 1.714285714rem;
	text-align: center;
}
.main-navigation li {
	margin-top: 24px;
	margin-top: 1.714285714rem;
	font-size: 12px;
	font-size: 0.857142857rem;
	line-height: 1.42857143;
}
.main-navigation a {
	color: #5e5e5e;
}
.main-navigation a:hover {
	color: #21759b;
}
.main-navigation div.nav-menu > ul {
	display: none;
}
.menu-toggle {
	display: inline-block;
}

/* Banner */

/* Sidebar */

/* Footer */
footer[role="contentinfo"] {
	border-top: 1px solid #ededed;
	clear: both;
	font-size: 12px;
	font-size: 0.857142857rem;
	line-height: 2;
	max-width: 960px;
	max-width: 68.571428571rem;
	margin-top: 24px;
	margin-top: 1.714285714rem;
	margin-left: auto;
	margin-right: auto;
	padding: 24px 0;
	padding: 1.714285714rem 0;
}
footer[role="contentinfo"] a {
	color: #686868;
}
footer[role="contentinfo"] a:hover {
	color: #21759b;
}


/* Minimum width of 600 pixels. */
@media screen and (min-width: 600px) {
	.site {
		margin: 0 auto;
		max-width: 960px;
		max-width: 68.571428571rem;
		overflow: hidden;
	}
	.site-header h1,
	.site-header h2 {
		text-align: left;
	}
	.site-header h1 {
		font-size: 26px;
		font-size: 1.857142857rem;
		line-height: 1.846153846;
		margin-bottom: 0;
	}
	.main-navigation div.nav-menu > ul {
		border-bottom: 1px solid #ededed;
		border-top: 1px solid #ededed;
		display: inline-block !important;
		text-align: left;
		width: 100%;
	}
	.main-navigation ul {
		margin: 0;
		text-indent: 0;
	}
	.main-navigation li a,
	.main-navigation li {
		display: inline-block;
		text-decoration: none;
	}
	.main-navigation li a {
		border-bottom: 0;
		color: #6a6a6a;
		line-height: 3.692307692;
		text-transform: uppercase;
		white-space: nowrap;
	}
	.main-navigation li a:hover {
		color: #000;
	}
	.main-navigation li {
		margin: 0 40px 0 0;
		margin: 0 2.857142857rem 0 0;
		position: relative;
	}
	.menu-toggle {
		display: none;
	}
}

/* Minimum width of 960 pixels. */
@media screen and (min-width: 960px) {
	body {
		background-color: #e6e6e6;
	}
	body .site {
		padding: 0 40px;
		padding: 0 2.857142857rem;
		margin-top: 48px;
		margin-top: 3.428571429rem;
		margin-bottom: 48px;
		margin-bottom: 3.428571429rem;
		box-shadow: 0 2px 6px rgba(100, 100, 100, 0.3);
	}
}


/* =Print
----------------------------------------------- */

@media print {
	body {
		background: none !important;
		color: #000;
		font-size: 10pt;
	}
	a {
		text-decoration: none;
	}
	.site {
		clear: both !important;
		display: block !important;
		float: none !important;
		max-width: 100%;
		position: relative !important;
	}
	.site-header {
		margin-bottom: 72px;
		margin-bottom: 5.142857143rem;
		text-align: left;
	}
	.site-header h1 {
		font-size: 21pt;
		line-height: 1;
		text-align: left;
	}
	.site-header h2 {
		color: #000;
		font-size: 10pt;
		text-align: left;
	}
	.site-header h1 a {
		color: #000;
	}
	#colophon,
	.main-navigation {
		display: none;
	}
	.wrapper {
		border-top: none;
		box-shadow: none;
	}
}
</style>


<style type="text/css">.recentcomments a{display:inline !important;padding:0 !important;margin:0 !important;}</style>
</head>
<body class="custom-font-enabled single-author">
<div class="hfeed site" id="page">
<header class="site-header" id="masthead" role="banner">
<hgroup>
<h1 class="site-title"><a href="#" rel="home" title="{{ keyword }}">{{ keyword }}</a></h1>
<h2 class="site-description">Just another WordPress site</h2>
</hgroup>
<nav class="main-navigation" id="site-navigation" role="navigation">
<h3 class="menu-toggle">Menu</h3>
<a class="assistive-text" href="#" title="Skip to content">Skip to content</a>
<div class="nav-menu"><ul><li><a href="#" title="Home">Home</a></li><li class="page_item page-item-2"><a href="#">Sample Page</a></li></ul></div>
</nav>
</header>
<div class="wrapper" id="main">
{{ text }}
	</div>
<footer id="colophon" role="contentinfo">
<div class="site-info">
</div>
</footer>
</div>


</body>
</html>";s:4:"text";s:3450:"What is the dot product of parallel vectors? Partial Differentiation; 4. The dot product of a column matrix with itself is a scalar, the square of the length of the vector it represents. Mathematicians are often a little weird. Limits and Continuity; 3. In mathematics, physics, and engineering, a Euclidean vector ... and length (the square root of the dot product of a vector by itself). Vectors and the dot product Avector ~vin R3 is an arrow. When at least one vector is of unit length the dot product is the length of the projection of the non-unit length vector onto the axis of the normalized vector (When they are both unit length, they are both moving the same amount in the direction of each other). AB if A(2;3;4)and B(2;1;1): Solution: ! The Chain Space Curves; 2. The Dot Product; 4. Functions of Several Variables; 2. 1. Learn how to find the length (or magnitude) of vectors, find unit vectors, & calculate simple dot products in linear algebra. 3. AB = h22;1+3;14i =h4;4;3i: Just like 2D vectors, for 3D vector addition, subtraction, and scalar mul-tiplication are de &ned similarly. Two vectors having the same length and direction are equal. Vectors can be added, subtracted, and multiplied by a scalar quite easily, but what about a vector times a vector? The cross product of two vectors a and b is a vector c, length (magnitude) of which numerically equals the area of the parallelogram based on vectors a and b as sides. Applications of the Vector Dot Product for Game Programming. Note that a vector consists of two elements: length and direction. The Dot Product & The Cross Product. Several problems with dot products, lengths, and distances of complex 3-dimensional vectors. Motion along a curve; 14 Partial Differentiation. This is because the angle is 0, so the cosine is 1. The dot product of two complex vectors is defined just like the dot product of real vectors. Detailed expanation is provided for each operation. The Dot Product ... Notice that the dot product of two vectors is a number and not a vector. Mathematicians are often a little weird. This chapter discusses two important facts: (1) The dot product of a column matrix with itself returns the square of the length of the vector it represents. If the two vectors are orthogonal (perpendicular) to each other, their dot product is zero. Find ! equal. There's actually two ways to do this: Dot ... We can always write a vector as a product of its length times its direction, ~v= j~vj ~v j~vj : 1. Dot Product Formula for Length. A) results in a value equal to the square of the vector's length. Lorentz Invariance and the 4-vector Dot Product The 4-vector is a powerful tool because the dot product of two 4-vectors is Lorentz Invariant. The surface area of a cube can be found by finding the length of any of the cube's ... Vector Dot Product; I am looking for some help in writing function below. Vectors and the dot product ... which have unit length and point ... We can always write a vector as a product of its length times its direction, Learn how to find the length (or magnitude) of vectors, find unit vectors, & calculate simple dot products in linear algebra. The length of a vector is the square root of the dot product of the vector with itself. The Cross Product; 5. The Dot Product is written using a central dot: ... is the magnitude (length) of vector b (2) The dot product of two column matrices that represent orthogonal vectors is zero. ";s:7:"keyword";s:30:"length of a vector dot product";s:7:"expired";i:-1;}