{"id":3996,"date":"2021-08-12T21:11:12","date_gmt":"2021-08-12T21:11:12","guid":{"rendered":"https:\/\/mathemerize.com\/?p=3996"},"modified":"2021-09-03T10:58:48","modified_gmt":"2021-09-03T05:28:48","slug":"state-polygon-law-of-vector-addition","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/state-polygon-law-of-vector-addition\/","title":{"rendered":"State Polygon Law of Vector Addition"},"content":{"rendered":"

Here, you will learn state polygon law of vector addition, subtraction of vectors and multiplication of vector by scalars.<\/p>\n

Let’s begin –<\/p>\n

Polygon law of vector Addition (Addition of more than two vectors)<\/h2>\n

Addition of more than two vectors is found to be by repetition of triangle law.<\/p>\n

Suppose we have to find the sum of five vectors \\(\\vec{a}\\), \\(\\vec{b}\\), \\(\\vec{c}\\), \\(\\vec{d}\\) and \\(\\vec{e}\\). If these vectors be represented by line segment \\(\\overrightarrow{OA}\\), \\(\\overrightarrow{AB}\\), \\(\\overrightarrow{BC}\\), \\(\\overrightarrow{CD}\\) and \\(\\overrightarrow{DE}\\) respectively, then their sum will be denoted by \\(\\overrightarrow{OE}\\). Th\u00eds is the vector represented by rest (last) side of the polygon OABCDE in reverse order. We can also make it clear this way :<\/p>\n

By triangle’s law<\/p>\n

i.e. \\(\\overrightarrow{OA}\\) + \\(\\overrightarrow{AB}\\) = \\(\\overrightarrow{OB}\\) \\(\\implies\\) \\(\\vec{a}\\) + \\(\\vec{b}\\) = \\(\\overrightarrow{OB}\\)\"polygon<\/p>\n

\\(\\overrightarrow{OB}\\) + \\(\\vec{c}\\) = \\(\\overrightarrow{OC}\\)\u00a0 \\(\\implies\\) (\\(\\vec{a}\\) + \\(\\vec{b}\\)) = \\(\\overrightarrow{OC}\\)<\/p>\n

\u00a0\\(\\overrightarrow{OC}\\) + \\(\\vec{d}\\) = \\(\\overrightarrow{OD}\\) \\(\\implies\\) \u00a0(\\(\\vec{a}\\) + \\(\\vec{b}\\) + \\(\\vec{c}\\)) +\\(\\vec{d}\\) = \\(\\overrightarrow{OD}\\)<\/p>\n

i.e. \\(\\overrightarrow{OD}\\) + \\(\\vec{e}\\) = \\(\\overrightarrow{OE}\\) \\(\\implies\\) \u00a0(\\(\\vec{a}\\) + \\(\\vec{b}\\) +\\(\\vec{c}\\) + \\(\\vec{d}\\)) + \\(\\vec{e}\\) = \\(\\overrightarrow{OE}\\)<\/p>\n

Here, we see that \\(\\overrightarrow{OE}\\) isrepresented by the line segment joining the initial point O of the first vector \\(\\vec{a}\\) and the final point of the last vector \\(\\vec{e}\\).<\/p>\n

In order to find the sum of more that two vectors by this method, a polygon is formed. Therefore this method is known as the polygon law of addition.<\/strong><\/p>\n

Subtraction of Vectors<\/h2>\n

Vector -\\(\\vec{b}\\) has length equals to vector b but its direction is opposite. Subtraction of vector \\(\\vec{a}\\) and \\(\\vec{b}\\) is defined as addition of \\(\\vec{a}\\) and (-\\(\\vec{b}\\)). It is written as follows :<\/p>\n

\\(\\vec{a}\\) – \\(\\vec{b}\\) = \\(\\vec{a}\\) + (-\\(\\vec{b}\\))<\/p>\n

Multiplication of vector by scalars<\/h2>\n

If \\(\\vec{a}\\) is a vector & m is a scalar, then m(\\(\\vec{a}\\)) is a vector parallel to \\(\\vec{a}\\) whose modulus is |m| times that of \\(\\vec{a}\\). This multiplication is called SCALAR MULTIPLICATION. If \\(\\vec{a}\\) & \\(\\vec{b}\\) are vectors & m, n are scalars, then :<\/p>\n

(1)\u00a0 m(\\(\\vec{a}\\)) = (\\(\\vec{a}\\))m = m(\\(\\vec{a}\\))<\/p>\n

(2)\u00a0 m(n\\(\\vec{a}\\)) = n(m\\(\\vec{a}\\)) = (mn)\\(\\vec{a}\\)<\/p>\n

(3)\u00a0 (m + n)\\(\\vec{a}\\) = m\\(\\vec{a}\\) + m\\(\\vec{a}\\)<\/p>\n

(4)\u00a0 m(\\(\\vec{a}\\) + \\(\\vec{b}\\)) = m\\(\\vec{a}\\) + m\\(\\vec{b}\\)<\/p>\n

Hope you learnt state polygon law of vector addition, subtraction of vectors and multiplication of vector by scalars. To learn more practice more question and get ahead in competition. Good Luck!<\/p>\n\n\n

\n
Next – Definition of Collinear Vectors and Coplanar Vectors<\/a><\/div>\n<\/div>\n\n\n\n
\n
Previous – Triangle Law of Addition of Vectors | Parallelogram Law<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Here, you will learn state polygon law of vector addition, subtraction of vectors and multiplication of vector by scalars. Let’s begin – Polygon law of vector Addition (Addition of more than two vectors) Addition of more than two vectors is found to be by repetition of triangle law. Suppose we have to find the sum …<\/p>\n

State Polygon Law of Vector Addition<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[33],"tags":[],"yoast_head":"\nState Polygon Law of Vector Addition - Mathemerize<\/title>\n<meta name=\"description\" content=\"In this post, you will learn state polygon law of vector addition, subtraction of vectors and multiplication of vector by scalars.\" \/>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathemerize.com\/state-polygon-law-of-vector-addition\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"State Polygon Law of Vector Addition - Mathemerize\" \/>\n<meta property=\"og:description\" content=\"In this post, you will learn state polygon law of vector addition, subtraction of vectors and multiplication of vector by scalars.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathemerize.com\/state-polygon-law-of-vector-addition\/\" \/>\n<meta property=\"og:site_name\" content=\"Mathemerize\" \/>\n<meta property=\"article:published_time\" content=\"2021-08-12T21:11:12+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2021-09-03T05:28:48+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/mathemerize.com\/wp-content\/uploads\/2021\/08\/polygon-law.png\" \/>\n<meta name=\"author\" content=\"mathemerize\" \/>\n<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n<meta name=\"twitter:label1\" content=\"Written by\" \/>\n\t<meta name=\"twitter:data1\" content=\"mathemerize\" \/>\n\t<meta name=\"twitter:label2\" content=\"Est. reading time\" \/>\n\t<meta name=\"twitter:data2\" content=\"2 minutes\" \/>\n<script type=\"application\/ld+json\" class=\"yoast-schema-graph\">{\"@context\":\"https:\/\/schema.org\",\"@graph\":[{\"@type\":\"Article\",\"@id\":\"https:\/\/mathemerize.com\/state-polygon-law-of-vector-addition\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathemerize.com\/state-polygon-law-of-vector-addition\/\"},\"author\":{\"name\":\"mathemerize\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df\"},\"headline\":\"State Polygon Law of Vector Addition\",\"datePublished\":\"2021-08-12T21:11:12+00:00\",\"dateModified\":\"2021-09-03T05:28:48+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathemerize.com\/state-polygon-law-of-vector-addition\/\"},\"wordCount\":458,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/mathemerize.com\/#organization\"},\"articleSection\":[\"Vectors\"],\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/mathemerize.com\/state-polygon-law-of-vector-addition\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathemerize.com\/state-polygon-law-of-vector-addition\/\",\"url\":\"https:\/\/mathemerize.com\/state-polygon-law-of-vector-addition\/\",\"name\":\"State Polygon Law of Vector Addition - Mathemerize\",\"isPartOf\":{\"@id\":\"https:\/\/mathemerize.com\/#website\"},\"datePublished\":\"2021-08-12T21:11:12+00:00\",\"dateModified\":\"2021-09-03T05:28:48+00:00\",\"description\":\"In this post, you will learn state polygon law of vector addition, subtraction of vectors and multiplication of vector by scalars.\",\"breadcrumb\":{\"@id\":\"https:\/\/mathemerize.com\/state-polygon-law-of-vector-addition\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/mathemerize.com\/state-polygon-law-of-vector-addition\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/mathemerize.com\/state-polygon-law-of-vector-addition\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/mathemerize.com\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"State Polygon Law of Vector Addition\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/mathemerize.com\/#website\",\"url\":\"https:\/\/mathemerize.com\/\",\"name\":\"Mathemerize\",\"description\":\"Maths Tutorials - Study Math Online\",\"publisher\":{\"@id\":\"https:\/\/mathemerize.com\/#organization\"},\"potentialAction\":[{\"@type\":\"SearchAction\",\"target\":{\"@type\":\"EntryPoint\",\"urlTemplate\":\"https:\/\/mathemerize.com\/?s={search_term_string}\"},\"query-input\":\"required name=search_term_string\"}],\"inLanguage\":\"en-US\"},{\"@type\":\"Organization\",\"@id\":\"https:\/\/mathemerize.com\/#organization\",\"name\":\"Mathemerize\",\"url\":\"https:\/\/mathemerize.com\/\",\"logo\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/logo\/image\/\",\"url\":\"https:\/\/i1.wp.com\/mathemerize.com\/wp-content\/uploads\/2021\/05\/logo.png?fit=140%2C96&ssl=1\",\"contentUrl\":\"https:\/\/i1.wp.com\/mathemerize.com\/wp-content\/uploads\/2021\/05\/logo.png?fit=140%2C96&ssl=1\",\"width\":140,\"height\":96,\"caption\":\"Mathemerize\"},\"image\":{\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/logo\/image\/\"},\"sameAs\":[\"https:\/\/www.instagram.com\/mathemerize\/\"]},{\"@type\":\"Person\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df\",\"name\":\"mathemerize\",\"image\":{\"@type\":\"ImageObject\",\"inLanguage\":\"en-US\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/image\/\",\"url\":\"https:\/\/secure.gravatar.com\/avatar\/f0649d8b9c9f4ba7f1682b12d040d2a3?s=96&d=mm&r=g\",\"contentUrl\":\"https:\/\/secure.gravatar.com\/avatar\/f0649d8b9c9f4ba7f1682b12d040d2a3?s=96&d=mm&r=g\",\"caption\":\"mathemerize\"},\"sameAs\":[\"https:\/\/mathemerize.com\"],\"url\":\"https:\/\/mathemerize.com\/author\/mathemerize\/\"}]}<\/script>\n<!-- \/ Yoast SEO plugin. -->","yoast_head_json":{"title":"State Polygon Law of Vector Addition - Mathemerize","description":"In this post, you will learn state polygon law of vector addition, subtraction of vectors and multiplication of vector by scalars.","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:\/\/mathemerize.com\/state-polygon-law-of-vector-addition\/","og_locale":"en_US","og_type":"article","og_title":"State Polygon Law of Vector Addition - Mathemerize","og_description":"In this post, you will learn state polygon law of vector addition, subtraction of vectors and multiplication of vector by scalars.","og_url":"https:\/\/mathemerize.com\/state-polygon-law-of-vector-addition\/","og_site_name":"Mathemerize","article_published_time":"2021-08-12T21:11:12+00:00","article_modified_time":"2021-09-03T05:28:48+00:00","og_image":[{"url":"https:\/\/mathemerize.com\/wp-content\/uploads\/2021\/08\/polygon-law.png"}],"author":"mathemerize","twitter_card":"summary_large_image","twitter_misc":{"Written by":"mathemerize","Est. reading time":"2 minutes"},"schema":{"@context":"https:\/\/schema.org","@graph":[{"@type":"Article","@id":"https:\/\/mathemerize.com\/state-polygon-law-of-vector-addition\/#article","isPartOf":{"@id":"https:\/\/mathemerize.com\/state-polygon-law-of-vector-addition\/"},"author":{"name":"mathemerize","@id":"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df"},"headline":"State Polygon Law of Vector Addition","datePublished":"2021-08-12T21:11:12+00:00","dateModified":"2021-09-03T05:28:48+00:00","mainEntityOfPage":{"@id":"https:\/\/mathemerize.com\/state-polygon-law-of-vector-addition\/"},"wordCount":458,"commentCount":0,"publisher":{"@id":"https:\/\/mathemerize.com\/#organization"},"articleSection":["Vectors"],"inLanguage":"en-US","potentialAction":[{"@type":"CommentAction","name":"Comment","target":["https:\/\/mathemerize.com\/state-polygon-law-of-vector-addition\/#respond"]}]},{"@type":"WebPage","@id":"https:\/\/mathemerize.com\/state-polygon-law-of-vector-addition\/","url":"https:\/\/mathemerize.com\/state-polygon-law-of-vector-addition\/","name":"State Polygon Law of Vector Addition - Mathemerize","isPartOf":{"@id":"https:\/\/mathemerize.com\/#website"},"datePublished":"2021-08-12T21:11:12+00:00","dateModified":"2021-09-03T05:28:48+00:00","description":"In this post, you will learn state polygon law of vector addition, subtraction of vectors and multiplication of vector by scalars.","breadcrumb":{"@id":"https:\/\/mathemerize.com\/state-polygon-law-of-vector-addition\/#breadcrumb"},"inLanguage":"en-US","potentialAction":[{"@type":"ReadAction","target":["https:\/\/mathemerize.com\/state-polygon-law-of-vector-addition\/"]}]},{"@type":"BreadcrumbList","@id":"https:\/\/mathemerize.com\/state-polygon-law-of-vector-addition\/#breadcrumb","itemListElement":[{"@type":"ListItem","position":1,"name":"Home","item":"https:\/\/mathemerize.com\/"},{"@type":"ListItem","position":2,"name":"State Polygon Law of Vector Addition"}]},{"@type":"WebSite","@id":"https:\/\/mathemerize.com\/#website","url":"https:\/\/mathemerize.com\/","name":"Mathemerize","description":"Maths Tutorials - Study Math Online","publisher":{"@id":"https:\/\/mathemerize.com\/#organization"},"potentialAction":[{"@type":"SearchAction","target":{"@type":"EntryPoint","urlTemplate":"https:\/\/mathemerize.com\/?s={search_term_string}"},"query-input":"required name=search_term_string"}],"inLanguage":"en-US"},{"@type":"Organization","@id":"https:\/\/mathemerize.com\/#organization","name":"Mathemerize","url":"https:\/\/mathemerize.com\/","logo":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/mathemerize.com\/#\/schema\/logo\/image\/","url":"https:\/\/i1.wp.com\/mathemerize.com\/wp-content\/uploads\/2021\/05\/logo.png?fit=140%2C96&ssl=1","contentUrl":"https:\/\/i1.wp.com\/mathemerize.com\/wp-content\/uploads\/2021\/05\/logo.png?fit=140%2C96&ssl=1","width":140,"height":96,"caption":"Mathemerize"},"image":{"@id":"https:\/\/mathemerize.com\/#\/schema\/logo\/image\/"},"sameAs":["https:\/\/www.instagram.com\/mathemerize\/"]},{"@type":"Person","@id":"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df","name":"mathemerize","image":{"@type":"ImageObject","inLanguage":"en-US","@id":"https:\/\/mathemerize.com\/#\/schema\/person\/image\/","url":"https:\/\/secure.gravatar.com\/avatar\/f0649d8b9c9f4ba7f1682b12d040d2a3?s=96&d=mm&r=g","contentUrl":"https:\/\/secure.gravatar.com\/avatar\/f0649d8b9c9f4ba7f1682b12d040d2a3?s=96&d=mm&r=g","caption":"mathemerize"},"sameAs":["https:\/\/mathemerize.com"],"url":"https:\/\/mathemerize.com\/author\/mathemerize\/"}]}},"jetpack_featured_media_url":"","_links":{"self":[{"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts\/3996"}],"collection":[{"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/comments?post=3996"}],"version-history":[{"count":5,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts\/3996\/revisions"}],"predecessor-version":[{"id":4976,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/posts\/3996\/revisions\/4976"}],"wp:attachment":[{"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/media?parent=3996"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/categories?post=3996"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mathemerize.com\/wp-json\/wp\/v2\/tags?post=3996"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}