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:3700:"Find the signed area spanned by two vectors. This property provides a simple method to test the condition of orthogonality. If they are in the opposite direction, then the dot product is negative. Algebraically, the dot product is the sum of the products of the corresponding entries of the two sequences of numbers. As the cosine of 90 is zero, the dot product of two orthogonal(perpendicular) vectors is always zero. Let's stick to $\mathbb{R}^2$. Dot Product and Perpendicular Vectors. Take the dot product of our two vectors to find the answer: Using our given vectors: Thus our two vectors are perpendicular. The dot product gives us a very nice method for determining if two vectors are perpendicular and it will give another method for determining when two vectors are parallel. (Since vectors have no location, it really makes little sense to talk about two vectors intersecting.) If the Dot Product is +1, the unit vectors are both pointing in the same direction. The way you always deal with issues of perpendicular vectors is with the dot product. In this final section of this chapter we will look at the cross product of two vectors. Multiply two vectors when only perpendicular cross-terms make a contribution (such as finding torque). This formula relates the dot product of a vector with the ... radians). Vector dot product = 0 for perpendicular vectors. Ex 12.3.16 Use the dot product to find a non-zero vector ... Ex 12.3.21 Let $\bf x$ and $\bf y$ be perpendicular vectors. To construct a vector that is perpendicular to another given vector, you can use techniques based on the dot-product and cross-product of vectors. Now, if two vectors are orthogonal then we know that the angle between them is 90 In this final section of this chapter we will look at the cross product of two vectors. If the Dot Product is -1, the unit vectors are pointing in opposite directions. Lecture 1: Dot Product ... what you should remember is that two vectors have a dot product ... we have a very fast way of checking whether two vectors are perpendicular. Vectors Dot Product - Vectors and Calculus Video Class - Vectors and Calculus Video Class for IIT JEE exams preparation and ... Vectors are perpendicular to each other. The dot product of the two column matrices that represent them is zero. DOT PRODUCT IN THREE DIMENSIONS. The "perp dot product" for and vectors in the plane is a modification of the two-dimensional dot product in which is replaced by the perpendicular vector rotated to the left defined by Hill (1994). Find the direction perpendicular to two given vectors. Use vectors and dot products to prove: if the diagonals of a rectangle are perpendicular, then the rectangle is a square. First notice that if one vector lies along the $x$ axis $u = x\hat{i}$ and the other $v = y\hat{j}$ lies along the $y$ axis, then their dot product is zero. Two vectors are perpendicular if their dot product is zero, and parallel if their dot product is 1. Dot Product of Orthogonal Vectors. Determine if two vectors are orthogonal (checking for a dot product of 0 is likely faster though). where is the angle from vector to vector . The Dot Product works well in two dimensions. The dot product is a float value equal to the magnitudes of the two vectors multiplied together and then multiplied by the cosine of the angle between them. In this case, the vectors are perpendicular to ... Dot_and_Cross_Product_Review which vectors are perpendicular to each other? Only the relative orientation matters. Since the two vectors are to be perpendicular to each other,their dot product should be 0. If the Dot Product is zero, the unit vectors are perpendicular (at right-angles to each other). ";s:7:"keyword";s:36:"dot product of perpendicular vectors";s:7:"expired";i:-1;}