{"id":631,"date":"2011-09-08T08:51:12","date_gmt":"2011-09-08T12:51:12","guid":{"rendered":"http:\/\/aplusphysics.com\/wordpress\/regents\/mechanics\/vector-manipulation\/"},"modified":"2011-09-08T08:51:12","modified_gmt":"2011-09-08T12:51:12","slug":"vector-manipulation","status":"publish","type":"post","link":"https:\/\/aplusphysics.com\/wordpress\/regents\/mechanics\/vector-manipulation\/","title":{"rendered":"Vector Manipulation"},"content":{"rendered":"<p>Quantities in physics are used to represent real-world measurements, and therefore physicists use these quantities as tools to better understand the world.&#160; In examining these quantities, there are times when just a number, with a unit, can completely describe a situation.&#160; These numbers, which have a magnitude, or size, only are known as scalars.&#160; Examples of scalars include quantities such as temperature, mass, and time.&#160; At other times, a quantity is more descriptive if it also includes a direction.&#160; These quantities which have both a magnitude and direction are known as vectors.&#160; Vector quantities you may be familiar with include force, velocity, and acceleration.<\/p>\n<p>Most students will be familiar with scalars, but to many, vectors may be a new and confusing concept.&#160; By learning just a few rules for dealing with vectors, though, you\u2019ll find that they are a powerful tool for problem solving.<\/p>\n<p><img loading=\"lazy\" decoding=\"async\" style=\"display: inline; margin-left: 0px; margin-right: 0px\" alt=\"Vector Magnitudes\" align=\"right\" src=\"http:\/\/www.aplusphysics.com\/courses\/regents\/mathreview\/images\/Vector_Magnitudes.gif\" width=\"218\" height=\"118\" \/><\/p>\n<p>Vectors are often represented as arrows, with the length of the arrow indicating the magnitude of the quantity, and the direction of the arrow indicating the direction of the vector.&#160; In the figure at right, vector <strong>B<\/strong> has a magnitude greater than that of vector<strong> A<\/strong>.&#160; Vectors <strong>A<\/strong> and <strong>B<\/strong> point in the same direction, however.&#160; It\u2019s also important to note that vectors can be moved anywhere in space.&#160; The positions of <strong>A<\/strong> and <strong>B<\/strong> could be reversed, and the individual vectors would retain their values of magnitude and direction.&#160; This makes adding vectors very straightforward! <\/p>\n<p><a href=\"http:\/\/aplusphysics.com\/wordpress\/regents\/wp-content\/uploads\/2011\/09\/image13.png\"><img loading=\"lazy\" decoding=\"async\" style=\"border-bottom: 0px; border-left: 0px; display: inline; margin-left: 0px; border-top: 0px; margin-right: 0px; border-right: 0px\" title=\"image\" border=\"0\" alt=\"image\" align=\"right\" src=\"http:\/\/aplusphysics.com\/wordpress\/regents\/wp-content\/uploads\/2011\/09\/image_thumb13.png\" width=\"244\" height=\"139\" \/><\/a> To add vectors <strong>A<\/strong> and <strong>B<\/strong>, all we have to do is line them up so that the tip of the first vector touches the tail of the second vector.&#160; Then, to find the sum of the vectors, known as the resultant, all we have to do is draw a straight line from the start of the first vector to the end of the last vector.&#160; This method works with any number of vectors.<\/p>\n<p>So then, how do we subtract two vectors?&#160; Let\u2019s try it by subtracting <strong>B<\/strong> from <strong>A<\/strong>. We could rewrite the expression <strong>A &#8211; B<\/strong> as <strong>A<\/strong> + <strong>-B<\/strong>.&#160; Now it becomes an addition problem, we just have to figure out how to express \u2013<strong>B<\/strong>.&#160; This is easier than it sounds \u2013 to find the opposite of a vector, we just point the vector in the opposite direction.&#160; Therefore, we can use what we already know about the addition of vectors to find the resultant of <strong>A<\/strong>&#8211;<strong>B<\/strong>.<\/p>\n<p><a href=\"http:\/\/aplusphysics.com\/wordpress\/regents\/wp-content\/uploads\/2011\/09\/image14.png\"><img loading=\"lazy\" decoding=\"async\" style=\"border-bottom: 0px; border-left: 0px; display: inline; border-top: 0px; border-right: 0px\" title=\"image\" border=\"0\" alt=\"image\" src=\"http:\/\/aplusphysics.com\/wordpress\/regents\/wp-content\/uploads\/2011\/09\/image_thumb14.png\" width=\"244\" height=\"118\" \/><\/a> <\/p>\n<p>&#160;<\/p>\n<h5>Components of Vectors<\/h5>\n<p>We\u2019ll learn more about vectors as we go, but before we move on, there\u2019s one more skill we need to learn. Vectors at angles can be challenging to deal with. By transforming a<img loading=\"lazy\" decoding=\"async\" style=\"display: inline; margin-left: 0px; margin-right: 0px\" alt=\"vectorcomponents\" align=\"right\" src=\"http:\/\/www.aplusphysics.com\/courses\/regents\/mathreview\/images\/VectorComponents.gif\" width=\"307\" height=\"157\" \/> vector at an angle into two vectors, one parallel to the x-axis and one parallel to the y-axis, we can greatly simplify problem solving.&#160; To break a vector up into its components, we can use our basic trig functions. To help us out even further, the Regents Physics Reference Table includes the exact formulas we need to determine the x- and y-components of any vector if we know that vector\u2019s magnitude and direction.<\/p>\n<\/p>\n<p><a href=\"http:\/\/aplusphysics.com\/wordpress\/regents\/wp-content\/uploads\/2011\/09\/image15.png\"><img loading=\"lazy\" decoding=\"async\" style=\"border-bottom: 0px; border-left: 0px; display: inline; border-top: 0px; border-right: 0px\" title=\"image\" border=\"0\" alt=\"image\" src=\"http:\/\/aplusphysics.com\/wordpress\/regents\/wp-content\/uploads\/2011\/09\/image_thumb15.png\" width=\"593\" height=\"382\" \/><\/a> <\/p>\n<p>In similar fashion, we can use the components of a vector in order to build the original vector. Graphically, if we line up the component vectors tip-to-tail, the original vector runs from the starting point of the first vector to the ending point of the last vector. To determine the magnitude of the resulting vector algebraically, just apply the Pythagorean Theorem!<\/p>\n<p><a href=\"http:\/\/aplusphysics.com\/wordpress\/regents\/wp-content\/uploads\/2011\/09\/image16.png\"><img loading=\"lazy\" decoding=\"async\" style=\"border-bottom: 0px; border-left: 0px; display: inline; border-top: 0px; border-right: 0px\" title=\"image\" border=\"0\" alt=\"image\" src=\"http:\/\/aplusphysics.com\/wordpress\/regents\/wp-content\/uploads\/2011\/09\/image_thumb16.png\" width=\"597\" height=\"355\" \/><\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Quantities in physics are used to represent real-world measurements, and therefore physicists use these quantities as tools to better understand the world.&#160; In examining these quantities, there are times when just a number, with a unit, can completely describe a <a class=\"more-link\" href=\"https:\/\/aplusphysics.com\/wordpress\/regents\/mechanics\/vector-manipulation\/\">Continue reading <span class=\"screen-reader-text\">  Vector Manipulation<\/span><span class=\"meta-nav\">&rarr;<\/span><\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[8,266,6],"tags":[290,289,46],"class_list":["post-631","post","type-post","status-publish","format-standard","hentry","category-kinematics","category-math","category-mechanics","tag-components","tag-pythagorean-theorem","tag-vectors"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v28.2 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Vector Manipulation - Regents Physics<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/aplusphysics.com\/wordpress\/regents\/mechanics\/vector-manipulation\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Vector Manipulation - Regents Physics\" \/>\n<meta property=\"og:description\" content=\"Quantities in physics are used to represent real-world measurements, and therefore physicists use these quantities as tools to better understand the world.&#160; In examining these quantities, there are times when just a number, with a unit, can completely describe a Continue reading  Vector Manipulation&rarr;\" \/>\n<meta property=\"og:url\" content=\"https:\/\/aplusphysics.com\/wordpress\/regents\/mechanics\/vector-manipulation\/\" \/>\n<meta property=\"og:site_name\" content=\"Regents Physics\" \/>\n<meta property=\"article:publisher\" content=\"https:\/\/www.facebook.com\/aplusphysics\" \/>\n<meta property=\"article:published_time\" content=\"2011-09-08T12:51:12+00:00\" \/>\n<meta property=\"og:image\" content=\"http:\/\/www.aplusphysics.com\/courses\/regents\/mathreview\/images\/Vector_Magnitudes.gif\" \/>\n<meta name=\"author\" content=\"admin\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:creator\" content=\"@aplusphysics\" \/>\n<meta name=\"twitter:site\" content=\"@aplusphysics\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"admin\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"3 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\\\/\\\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\\\/\\\/aplusphysics.com\\\/wordpress\\\/regents\\\/mechanics\\\/vector-manipulation\\\/#article\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/aplusphysics.com\\\/wordpress\\\/regents\\\/mechanics\\\/vector-manipulation\\\/\"},\"author\":{\"name\":\"admin\",\"@id\":\"https:\\\/\\\/aplusphysics.com\\\/wordpress\\\/regents\\\/#\\\/schema\\\/person\\\/c2ac2abe916d9f213b6cb0d57c685d46\"},\"headline\":\"Vector Manipulation\",\"datePublished\":\"2011-09-08T12:51:12+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\\\/\\\/aplusphysics.com\\\/wordpress\\\/regents\\\/mechanics\\\/vector-manipulation\\\/\"},\"wordCount\":576,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\\\/\\\/aplusphysics.com\\\/wordpress\\\/regents\\\/#organization\"},\"image\":{\"@id\":\"https:\\\/\\\/aplusphysics.com\\\/wordpress\\\/regents\\\/mechanics\\\/vector-manipulation\\\/#primaryimage\"},\"thumbnailUrl\":\"http:\\\/\\\/www.aplusphysics.com\\\/courses\\\/regents\\\/mathreview\\\/images\\\/Vector_Magnitudes.gif\",\"keywords\":[\"components\",\"Pythagorean Theorem\",\"vectors\"],\"articleSection\":[\"Kinematics\",\"Math\",\"Mechanics\"],\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\\\/\\\/aplusphysics.com\\\/wordpress\\\/regents\\\/mechanics\\\/vector-manipulation\\\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\\\/\\\/aplusphysics.com\\\/wordpress\\\/regents\\\/mechanics\\\/vector-manipulation\\\/\",\"url\":\"https:\\\/\\\/aplusphysics.com\\\/wordpress\\\/regents\\\/mechanics\\\/vector-manipulation\\\/\",\"name\":\"Vector Manipulation - Regents Physics\",\"isPartOf\":{\"@id\":\"https:\\\/\\\/aplusphysics.com\\\/wordpress\\\/regents\\\/#website\"},\"primaryImageOfPage\":{\"@id\":\"https:\\\/\\\/aplusphysics.com\\\/wordpress\\\/regents\\\/mechanics\\\/vector-manipulation\\\/#primaryimage\"},\"image\":{\"@id\":\"https:\\\/\\\/aplusphysics.com\\\/wordpress\\\/regents\\\/mechanics\\\/vector-manipulation\\\/#primaryimage\"},\"thumbnailUrl\":\"http:\\\/\\\/www.aplusphysics.com\\\/courses\\\/regents\\\/mathreview\\\/images\\\/Vector_Magnitudes.gif\",\"datePublished\":\"2011-09-08T12:51:12+00:00\",\"breadcrumb\":{\"@id\":\"https:\\\/\\\/aplusphysics.com\\\/wordpress\\\/regents\\\/mechanics\\\/vector-manipulation\\\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\\\/\\\/aplusphysics.com\\\/wordpress\\\/regents\\\/mechanics\\\/vector-manipulation\\\/\"]}]},{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\\\/\\\/aplusphysics.com\\\/wordpress\\\/regents\\\/mechanics\\\/vector-manipulation\\\/#primaryimage\",\"url\":\"http:\\\/\\\/www.aplusphysics.com\\\/courses\\\/regents\\\/mathreview\\\/images\\\/Vector_Magnitudes.gif\",\"contentUrl\":\"http:\\\/\\\/www.aplusphysics.com\\\/courses\\\/regents\\\/mathreview\\\/images\\\/Vector_Magnitudes.gif\"},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\\\/\\\/aplusphysics.com\\\/wordpress\\\/regents\\\/mechanics\\\/vector-manipulation\\\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\\\/\\\/aplusphysics.com\\\/wordpress\\\/regents\\\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Vector Manipulation\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\\\/\\\/aplusphysics.com\\\/wordpress\\\/regents\\\/#website\",\"url\":\"https:\\\/\\\/aplusphysics.com\\\/wordpress\\\/regents\\\/\",\"name\":\"Regents Physics\",\"description\":\"\",\"publisher\":{\"@id\":\"https:\\\/\\\/aplusphysics.com\\\/wordpress\\\/regents\\\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\\\/\\\/aplusphysics.com\\\/wordpress\\\/regents\\\/?s={search_term_string}\"},\"query-input\":{\"@type\":\"PropertyValueSpecification\",\"valueRequired\":true,\"valueName\":\"search_term_string\"}}],\"inLanguage\":\"en-US\"},{\"@type\":\"Organization\",\"@id\":\"https:\\\/\\\/aplusphysics.com\\\/wordpress\\\/regents\\\/#organization\",\"name\":\"APlusPhysics\",\"url\":\"https:\\\/\\\/aplusphysics.com\\\/wordpress\\\/regents\\\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\\\/\\\/aplusphysics.com\\\/wordpress\\\/regents\\\/#\\\/schema\\\/logo\\\/image\\\/\",\"url\":\"https:\\\/\\\/aplusphysics.com\\\/wordpress\\\/regents\\\/wp-content\\\/uploads\\\/2015\\\/06\\\/APlusPhysics_Logo_HDef.png\",\"contentUrl\":\"https:\\\/\\\/aplusphysics.com\\\/wordpress\\\/regents\\\/wp-content\\\/uploads\\\/2015\\\/06\\\/APlusPhysics_Logo_HDef.png\",\"width\":1500,\"height\":1069,\"caption\":\"APlusPhysics\"},\"image\":{\"@id\":\"https:\\\/\\\/aplusphysics.com\\\/wordpress\\\/regents\\\/#\\\/schema\\\/logo\\\/image\\\/\"},\"sameAs\":[\"https:\\\/\\\/www.facebook.com\\\/aplusphysics\",\"https:\\\/\\\/x.com\\\/aplusphysics\",\"https:\\\/\\\/www.linkedin.com\\\/in\\\/aplusphysics\\\/\",\"https:\\\/\\\/www.youtube.com\\\/user\\\/fizziksguy\"]},{\"@type\":\"Person\",\"@id\":\"https:\\\/\\\/aplusphysics.com\\\/wordpress\\\/regents\\\/#\\\/schema\\\/person\\\/c2ac2abe916d9f213b6cb0d57c685d46\",\"name\":\"admin\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/242edd616e1085518670004a090bc15c23eebb49a6b9191f1e1b23ea6d8567db?s=96&d=mm&r=g\",\"url\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/242edd616e1085518670004a090bc15c23eebb49a6b9191f1e1b23ea6d8567db?s=96&d=mm&r=g\",\"contentUrl\":\"https:\\\/\\\/secure.gravatar.com\\\/avatar\\\/242edd616e1085518670004a090bc15c23eebb49a6b9191f1e1b23ea6d8567db?s=96&d=mm&r=g\",\"caption\":\"admin\"},\"url\":\"https:\\\/\\\/aplusphysics.com\\\/wordpress\\\/regents\\\/author\\\/admin\\\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"Vector Manipulation - Regents Physics","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/aplusphysics.com\/wordpress\/regents\/mechanics\/vector-manipulation\/","og_locale":"en_US","og_type":"article","og_title":"Vector Manipulation - Regents Physics","og_description":"Quantities in physics are used to represent real-world measurements, and therefore physicists use these quantities as tools to better understand the world.&#160; In examining these quantities, there are times when just a number, with a unit, can completely describe a Continue reading  Vector Manipulation&rarr;","og_url":"https:\/\/aplusphysics.com\/wordpress\/regents\/mechanics\/vector-manipulation\/","og_site_name":"Regents Physics","article_publisher":"https:\/\/www.facebook.com\/aplusphysics","article_published_time":"2011-09-08T12:51:12+00:00","og_image":[{"url":"http:\/\/www.aplusphysics.com\/courses\/regents\/mathreview\/images\/Vector_Magnitudes.gif","type":"","width":"","height":""}],"author":"admin","twitter_card":"summary_large_image","twitter_creator":"@aplusphysics","twitter_site":"@aplusphysics","twitter_misc":{"Written by":"admin","Est. reading time":"3 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/aplusphysics.com\/wordpress\/regents\/mechanics\/vector-manipulation\/#article","isPartOf":{"@id":"https:\/\/aplusphysics.com\/wordpress\/regents\/mechanics\/vector-manipulation\/"},"author":{"name":"admin","@id":"https:\/\/aplusphysics.com\/wordpress\/regents\/#\/schema\/person\/c2ac2abe916d9f213b6cb0d57c685d46"},"headline":"Vector Manipulation","datePublished":"2011-09-08T12:51:12+00:00","mainEntityOfPage":{"@id":"https:\/\/aplusphysics.com\/wordpress\/regents\/mechanics\/vector-manipulation\/"},"wordCount":576,"commentCount":0,"publisher":{"@id":"https:\/\/aplusphysics.com\/wordpress\/regents\/#organization"},"image":{"@id":"https:\/\/aplusphysics.com\/wordpress\/regents\/mechanics\/vector-manipulation\/#primaryimage"},"thumbnailUrl":"http:\/\/www.aplusphysics.com\/courses\/regents\/mathreview\/images\/Vector_Magnitudes.gif","keywords":["components","Pythagorean Theorem","vectors"],"articleSection":["Kinematics","Math","Mechanics"],"inLanguage":"en-US","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/aplusphysics.com\/wordpress\/regents\/mechanics\/vector-manipulation\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/aplusphysics.com\/wordpress\/regents\/mechanics\/vector-manipulation\/","url":"https:\/\/aplusphysics.com\/wordpress\/regents\/mechanics\/vector-manipulation\/","name":"Vector Manipulation - Regents Physics","isPartOf":{"@id":"https:\/\/aplusphysics.com\/wordpress\/regents\/#website"},"primaryImageOfPage":{"@id":"https:\/\/aplusphysics.com\/wordpress\/regents\/mechanics\/vector-manipulation\/#primaryimage"},"image":{"@id":"https:\/\/aplusphysics.com\/wordpress\/regents\/mechanics\/vector-manipulation\/#primaryimage"},"thumbnailUrl":"http:\/\/www.aplusphysics.com\/courses\/regents\/mathreview\/images\/Vector_Magnitudes.gif","datePublished":"2011-09-08T12:51:12+00:00","breadcrumb":{"@id":"https:\/\/aplusphysics.com\/wordpress\/regents\/mechanics\/vector-manipulation\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/aplusphysics.com\/wordpress\/regents\/mechanics\/vector-manipulation\/"]}]},{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/aplusphysics.com\/wordpress\/regents\/mechanics\/vector-manipulation\/#primaryimage","url":"http:\/\/www.aplusphysics.com\/courses\/regents\/mathreview\/images\/Vector_Magnitudes.gif","contentUrl":"http:\/\/www.aplusphysics.com\/courses\/regents\/mathreview\/images\/Vector_Magnitudes.gif"},{"@type":"BreadcrumbList","@id":"https:\/\/aplusphysics.com\/wordpress\/regents\/mechanics\/vector-manipulation\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/aplusphysics.com\/wordpress\/regents\/"},{"@type":"ListItem","position":2,"name":"Vector Manipulation"}]},{"@type":"WebSite","@id":"https:\/\/aplusphysics.com\/wordpress\/regents\/#website","url":"https:\/\/aplusphysics.com\/wordpress\/regents\/","name":"Regents Physics","description":"","publisher":{"@id":"https:\/\/aplusphysics.com\/wordpress\/regents\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/aplusphysics.com\/wordpress\/regents\/?s={search_term_string}"},"query-input":{"@type":"PropertyValueSpecification","valueRequired":true,"valueName":"search_term_string"}}],"inLanguage":"en-US"},{"@type":"Organization","@id":"https:\/\/aplusphysics.com\/wordpress\/regents\/#organization","name":"APlusPhysics","url":"https:\/\/aplusphysics.com\/wordpress\/regents\/","logo":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/aplusphysics.com\/wordpress\/regents\/#\/schema\/logo\/image\/","url":"https:\/\/aplusphysics.com\/wordpress\/regents\/wp-content\/uploads\/2015\/06\/APlusPhysics_Logo_HDef.png","contentUrl":"https:\/\/aplusphysics.com\/wordpress\/regents\/wp-content\/uploads\/2015\/06\/APlusPhysics_Logo_HDef.png","width":1500,"height":1069,"caption":"APlusPhysics"},"image":{"@id":"https:\/\/aplusphysics.com\/wordpress\/regents\/#\/schema\/logo\/image\/"},"sameAs":["https:\/\/www.facebook.com\/aplusphysics","https:\/\/x.com\/aplusphysics","https:\/\/www.linkedin.com\/in\/aplusphysics\/","https:\/\/www.youtube.com\/user\/fizziksguy"]},{"@type":"Person","@id":"https:\/\/aplusphysics.com\/wordpress\/regents\/#\/schema\/person\/c2ac2abe916d9f213b6cb0d57c685d46","name":"admin","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/secure.gravatar.com\/avatar\/242edd616e1085518670004a090bc15c23eebb49a6b9191f1e1b23ea6d8567db?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/242edd616e1085518670004a090bc15c23eebb49a6b9191f1e1b23ea6d8567db?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/242edd616e1085518670004a090bc15c23eebb49a6b9191f1e1b23ea6d8567db?s=96&d=mm&r=g","caption":"admin"},"url":"https:\/\/aplusphysics.com\/wordpress\/regents\/author\/admin\/"}]}},"_links":{"self":[{"href":"https:\/\/aplusphysics.com\/wordpress\/regents\/wp-json\/wp\/v2\/posts\/631","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/aplusphysics.com\/wordpress\/regents\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/aplusphysics.com\/wordpress\/regents\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/aplusphysics.com\/wordpress\/regents\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/aplusphysics.com\/wordpress\/regents\/wp-json\/wp\/v2\/comments?post=631"}],"version-history":[{"count":0,"href":"https:\/\/aplusphysics.com\/wordpress\/regents\/wp-json\/wp\/v2\/posts\/631\/revisions"}],"wp:attachment":[{"href":"https:\/\/aplusphysics.com\/wordpress\/regents\/wp-json\/wp\/v2\/media?parent=631"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/aplusphysics.com\/wordpress\/regents\/wp-json\/wp\/v2\/categories?post=631"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/aplusphysics.com\/wordpress\/regents\/wp-json\/wp\/v2\/tags?post=631"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}