{"id":3994,"date":"2021-08-12T20:52:09","date_gmt":"2021-08-12T20:52:09","guid":{"rendered":"https:\/\/mathemerize.com\/?p=3994"},"modified":"2021-10-16T18:50:24","modified_gmt":"2021-10-16T13:20:24","slug":"triangle-law-of-addition-of-vectors","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/triangle-law-of-addition-of-vectors\/","title":{"rendered":"Triangle Law of Addition of Vectors | Parallelogram Law"},"content":{"rendered":"

Here, you will learn triangle law of addition of vectors and parallelogram law of addition of vectors and properties of vector addition.<\/p>\n

Let’s begin –<\/p>\n

Addition of Vectors <\/h2>\n

The vectors have magnitude as well as direction, therefore their addition is different than addition of real numbers.<\/p>\n

Let \\(\\vec{a}\\) and \\(\\vec{b}\\) be two vectors in a plane, which are represented by AB and CD. Their addition can be performed in the following two ways :<\/p>\n

Triangle Law of Addition of Vectors<\/h2>\n

If two vectors can be represented in magnitude and direction by the two sides of a triangle, taken in order, then their sum will be represented by the third side in reverse order.\"triangle<\/p>\n

Let O be the fixed point in the plane of vectors. Draw a line segment \\(\\overrightarrow{OE}\\) from O, equal and parallel to \\(\\overrightarrow{AB}\\), which represents the vector \\(\\vec{a}\\). Now from E, draw a line segment \\(\\overrightarrow{EF}\\) equal and parallel to \\(\\overrightarrow{CD}\\), which represents the vector \\(\\vec{b}\\). Line segment \\(\\overrightarrow{OF}\\) obtained by joining O and F represents the sum of vectors \\(\\vec{a}\\) and \\(\\vec{b}\\).<\/p>\n

i.e. \\(\\overrightarrow{OE}\\) + \\(\\overrightarrow{EF}\\) = \\(\\overrightarrow{OF}\\)<\/p>\n

or \\(\\vec{a}\\) + \\(\\vec{b}\\) = \\(\\overrightarrow{OF}\\)<\/p>\n

This method of addition of two vectors is called Triangle law of addition of vectors.<\/strong><\/p>\n

Parallelogram Law of Addition of Vectors<\/h2>\n

If two vectors be represented in magnitude and direction by the two adjacent sides of a parallelogram then their sum will be represented by the diagonal through the co-initial point.\"parallelogram<\/p>\n

Let \\(\\vec{a}\\) and \\(\\vec{b}\\) be vectors drawn from point O denoted by line segments \\(\\overrightarrow{OP}\\) and \\(\\overrightarrow{OQ}\\). Now complete the parallelogram OPRQ. Then the vector represented by the diagonal OR will represent the sum of the vectors \\(\\vec{a}\\) and \\(\\vec{b}\\).<\/p>\n

i.e. \\(\\overrightarrow{OP}\\) + \\(\\overrightarrow{OQ}\\) = \\(\\overrightarrow{OR}\\)<\/p>\n

or \\(\\vec{a}\\) + \\(\\vec{b}\\) = \\(\\overrightarrow{OR}\\)<\/p>\n

This method of addition of two vectors is called Parallelogram law of addition of vectors.<\/strong><\/p>\n

Properties of Vector Addition<\/h2>\n

(i)  \\(\\vec{a}\\) + \\(\\vec{b}\\) = \\(\\vec{b}\\) + \\(\\vec{a}\\) (Commutative)<\/p>\n

(ii)  (\\(\\vec{a}\\) + \\(\\vec{b}\\)) + \\(\\vec{c}\\) = \\(\\vec{a}\\) + (\\(\\vec{b}\\) + \\(\\vec{c}\\)) (associativity)<\/p>\n

(iii)  \\(\\vec{a}\\) + 0 = 0 + \\(\\vec{a}\\) (additive identity)<\/p>\n

(iv)  \\(\\vec{a}\\) + (-\\(\\vec{a}\\)) = 0 (additive inverse)<\/p>\n\n\n

\n
Next – State Polygon Law of Vector Addition<\/a><\/div>\n<\/div>\n\n\n\n
\n
Previous – Vector Quantities and Scalar Quantities<\/a><\/div>\n<\/div>\n","protected":false},"excerpt":{"rendered":"

Here, you will learn triangle law of addition of vectors and parallelogram law of addition of vectors and properties of vector addition. Let’s begin – Addition of Vectors  The vectors have magnitude as well as direction, therefore their addition is different than addition of real numbers. Let \\(\\vec{a}\\) and \\(\\vec{b}\\) be two vectors in a …<\/p>\n

Triangle Law of Addition of Vectors | Parallelogram Law<\/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":"\nTriangle Law of Addition of Vectors | Parallelogram Law<\/title>\n<meta name=\"description\" content=\"In this post, you will learn triangle law of addition of vectors and parallelogram law of addition of vectors.\" \/>\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\/triangle-law-of-addition-of-vectors\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Triangle Law of Addition of Vectors | Parallelogram Law\" \/>\n<meta property=\"og:description\" content=\"In this post, you will learn triangle law of addition of vectors and parallelogram law of addition of vectors.\" \/>\n<meta property=\"og:url\" content=\"https:\/\/mathemerize.com\/triangle-law-of-addition-of-vectors\/\" \/>\n<meta property=\"og:site_name\" content=\"Mathemerize\" \/>\n<meta property=\"article:published_time\" content=\"2021-08-12T20:52:09+00:00\" \/>\n<meta property=\"article:modified_time\" content=\"2021-10-16T13:20:24+00:00\" \/>\n<meta property=\"og:image\" content=\"https:\/\/mathemerize.com\/wp-content\/uploads\/2021\/08\/triangle-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\/triangle-law-of-addition-of-vectors\/#article\",\"isPartOf\":{\"@id\":\"https:\/\/mathemerize.com\/triangle-law-of-addition-of-vectors\/\"},\"author\":{\"name\":\"mathemerize\",\"@id\":\"https:\/\/mathemerize.com\/#\/schema\/person\/104c8bc54f90618130a6665299bc55df\"},\"headline\":\"Triangle Law of Addition of Vectors | Parallelogram Law\",\"datePublished\":\"2021-08-12T20:52:09+00:00\",\"dateModified\":\"2021-10-16T13:20:24+00:00\",\"mainEntityOfPage\":{\"@id\":\"https:\/\/mathemerize.com\/triangle-law-of-addition-of-vectors\/\"},\"wordCount\":399,\"commentCount\":0,\"publisher\":{\"@id\":\"https:\/\/mathemerize.com\/#organization\"},\"articleSection\":[\"Vectors\"],\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"CommentAction\",\"name\":\"Comment\",\"target\":[\"https:\/\/mathemerize.com\/triangle-law-of-addition-of-vectors\/#respond\"]}]},{\"@type\":\"WebPage\",\"@id\":\"https:\/\/mathemerize.com\/triangle-law-of-addition-of-vectors\/\",\"url\":\"https:\/\/mathemerize.com\/triangle-law-of-addition-of-vectors\/\",\"name\":\"Triangle Law of Addition of Vectors | Parallelogram Law\",\"isPartOf\":{\"@id\":\"https:\/\/mathemerize.com\/#website\"},\"datePublished\":\"2021-08-12T20:52:09+00:00\",\"dateModified\":\"2021-10-16T13:20:24+00:00\",\"description\":\"In this post, you will learn triangle law of addition of vectors and parallelogram law of addition of vectors.\",\"breadcrumb\":{\"@id\":\"https:\/\/mathemerize.com\/triangle-law-of-addition-of-vectors\/#breadcrumb\"},\"inLanguage\":\"en-US\",\"potentialAction\":[{\"@type\":\"ReadAction\",\"target\":[\"https:\/\/mathemerize.com\/triangle-law-of-addition-of-vectors\/\"]}]},{\"@type\":\"BreadcrumbList\",\"@id\":\"https:\/\/mathemerize.com\/triangle-law-of-addition-of-vectors\/#breadcrumb\",\"itemListElement\":[{\"@type\":\"ListItem\",\"position\":1,\"name\":\"Home\",\"item\":\"https:\/\/mathemerize.com\/\"},{\"@type\":\"ListItem\",\"position\":2,\"name\":\"Triangle Law of Addition of Vectors | Parallelogram Law\"}]},{\"@type\":\"WebSite\",\"@id\":\"https:\/\/mathemerize.com\/#website\",\"url\":\"https:\/\/mathemerize.com\/\",\"name\":\"Mathemerize\",\"description\":\"Maths Tutorials - 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