{"id":154128,"date":"2022-03-25T23:11:27","date_gmt":"2022-03-25T17:41:27","guid":{"rendered":"https:\/\/infinitylearn.com\/surge\/parallelogram-law-law-of-addition-law-of-vectors-procedure-and-proofs\/"},"modified":"2022-12-27T13:02:51","modified_gmt":"2022-12-27T07:32:51","slug":"parallelogram-law-law-of-addition-law-of-vectors-procedure-and-proofs","status":"publish","type":"post","link":"https:\/\/infinitylearn.com\/surge\/maths\/parallelogram-law\/","title":{"rendered":"Parallelogram Law &#8211; Law of Addition, Law of vectors, Procedure and Proofs"},"content":{"rendered":"<div id=\"ez-toc-container\" class=\"ez-toc-v2_0_37 counter-hierarchy ez-toc-counter ez-toc-grey ez-toc-container-direction\">\n<div class=\"ez-toc-title-container\">\n<p class=\"ez-toc-title\">Table of Contents<\/p>\n<span class=\"ez-toc-title-toggle\"><a href=\"#\" class=\"ez-toc-pull-right ez-toc-btn ez-toc-btn-xs ez-toc-btn-default ez-toc-toggle\" style=\"display: none;\"><label for=\"item\" aria-label=\"Table of Content\"><span style=\"display: flex;align-items: center;width: 35px;height: 30px;justify-content: center;\"><svg style=\"fill: #999;color:#999\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" class=\"list-377408\" width=\"20px\" height=\"20px\" viewBox=\"0 0 24 24\" fill=\"none\"><path d=\"M6 6H4v2h2V6zm14 0H8v2h12V6zM4 11h2v2H4v-2zm16 0H8v2h12v-2zM4 16h2v2H4v-2zm16 0H8v2h12v-2z\" fill=\"currentColor\"><\/path><\/svg><svg style=\"fill: #999;color:#999\" class=\"arrow-unsorted-368013\" xmlns=\"http:\/\/www.w3.org\/2000\/svg\" width=\"10px\" height=\"10px\" viewBox=\"0 0 24 24\" version=\"1.2\" baseProfile=\"tiny\"><path d=\"M18.2 9.3l-6.2-6.3-6.2 6.3c-.2.2-.3.4-.3.7s.1.5.3.7c.2.2.4.3.7.3h11c.3 0 .5-.1.7-.3.2-.2.3-.5.3-.7s-.1-.5-.3-.7zM5.8 14.7l6.2 6.3 6.2-6.3c.2-.2.3-.5.3-.7s-.1-.5-.3-.7c-.2-.2-.4-.3-.7-.3h-11c-.3 0-.5.1-.7.3-.2.2-.3.5-.3.7s.1.5.3.7z\"\/><\/svg><\/span><\/label><input type=\"checkbox\" id=\"item\"><\/a><\/span><\/div>\n<nav><ul class='ez-toc-list ez-toc-list-level-1' style='display:block'><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-1\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/parallelogram-law\/#What_is_Parallelogram\" title=\"What is Parallelogram?\">What is Parallelogram?<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-2\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/parallelogram-law\/#Parallelogram_Law_of_Addition\" title=\"Parallelogram Law of Addition\">Parallelogram Law of Addition<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-3\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/parallelogram-law\/#Parallelogram_Law_of_Vectors\" title=\"Parallelogram Law of Vectors\">Parallelogram Law of Vectors<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-4\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/parallelogram-law\/#Parallelogram_Law_of_Addition_of_Vectors_Procedure\" title=\"Parallelogram Law of Addition of Vectors Procedure\">Parallelogram Law of Addition of Vectors Procedure<\/a><\/li><li class='ez-toc-page-1 ez-toc-heading-level-2'><a class=\"ez-toc-link ez-toc-heading-5\" href=\"https:\/\/infinitylearn.com\/surge\/maths\/parallelogram-law\/#Parallelogram_Law_Proof\" title=\"Parallelogram Law Proof\">Parallelogram Law Proof<\/a><\/li><\/ul><\/nav><\/div>\n<h2><span class=\"ez-toc-section\" id=\"What_is_Parallelogram\"><\/span>What is Parallelogram?<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>Parallelogram Law &#8211; Law of Addition: A <a href=\"https:\/\/infinitylearn.com\/surge\/maths\/parallelogram-law\/\">parallelogram<\/a> is a quadrilateral with two pairs of parallel sides.<\/p>\n<p><img loading=\"lazy\" class=\"aligncenter wp-image-154127 size-full\" src=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/parallelogram-law-law-of-addition-law-of-vectors-procedure-and-proofs.jpg\" alt=\"Parallelogram Law - Law of Addition, Law of vectors, Procedure and Proofs\" width=\"606\" height=\"428\" srcset=\"https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/parallelogram-law-law-of-addition-law-of-vectors-procedure-and-proofs.jpg?v=1648230083 606w, https:\/\/infinitylearn.com\/surge\/wp-content\/uploads\/2022\/03\/parallelogram-law-law-of-addition-law-of-vectors-procedure-and-proofs-300x212.jpg?v=1648230083 300w\" sizes=\"(max-width: 606px) 100vw, 606px\" \/><\/p>\n<h2><span class=\"ez-toc-section\" id=\"Parallelogram_Law_of_Addition\"><\/span>Parallelogram Law of Addition<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>If two vectors are placed at right angles to each other, the resultant vector is the sum of the vectors. The magnitude of the resultant vector is the sum of the magnitudes of the vectors and the direction is the direction of the vector sum.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Parallelogram_Law_of_Vectors\"><\/span>Parallelogram Law of Vectors<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A parallelogram law of vectors states that the vector sum of two vectors is the diagonal of the parallelogram formed by them. The law is also known as the parallelogram law of addition.<\/p>\n<h2><span class=\"ez-toc-section\" id=\"Parallelogram_Law_of_Addition_of_Vectors_Procedure\"><\/span>Parallelogram Law of Addition of Vectors Procedure<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>To add two vectors using the parallelogram law of addition, follow these steps:<\/p>\n<ul>\n<li>Draw a diagram of the two vectors to be added. The vectors should be represented by two arrows, one for each vector.<\/li>\n<li>Label the start point of the first vector and the end point of the second vector.<\/li>\n<li>Draw a parallelogram using the two vectors as the sides. The vectors should be perpendicular to each other.<\/li>\n<li>Find the length of each vector and the angle between the vectors.<\/li>\n<li>Add the vectors together by finding the vector sum. This is the vector that points from the start point of the first vector to the end point of the second vector.<\/li>\n<li>Draw the vector sum as an arrow.<\/li>\n<\/ul>\n<h2><span class=\"ez-toc-section\" id=\"Parallelogram_Law_Proof\"><\/span>Parallelogram Law Proof<span class=\"ez-toc-section-end\"><\/span><\/h2>\n<p>A parallelogram is a quadrilateral with two pairs of parallel sides. The following theorem known as the parallelogram law.<\/p>\n<p>Theorem: The sum of the two opposite angles of a parallelogram is 180\u00b0.<\/p>\n<p>Proof:<\/p>\n<ul>\n<li>We will use the following definition:<\/li>\n<li>The angle between two lines is the angle between the lines when they considered to be rays.<\/li>\n<li>Let $\\angle A$ and $\\angle B$ be the angles opposite the respective sides of length $a$ and $b$.<\/li>\n<li>Since the two angles are opposite, they are supplementary. That is,<\/li>\n<li>$\\angle A + \\angle B = 180^{\\circ}$<\/li>\n<li>Now, we use the fact that the angles of a parallelogram are right angles. Hence,<\/li>\n<li>$\\angle A = 90^{\\circ}$ and $\\angle B = 90^{\\circ}$<\/li>\n<li>Therefore,<\/li>\n<li>$\\angle A + \\angle B = 180^{\\circ}$<\/li>\n<li>$\\angle A + \\angle B = 180^{\\circ}$<\/li>\n<\/ul>\n","protected":false},"excerpt":{"rendered":"<p>What is Parallelogram? Parallelogram Law &#8211; Law of Addition: A parallelogram is a quadrilateral with two pairs of parallel sides. [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_yoast_wpseo_focuskw":"Parallelogram Law - Law of Addition","_yoast_wpseo_title":"%%title%% %%page%%","_yoast_wpseo_metadesc":"Learn about Parallelogram Law topic of maths in details explained by subject experts on infinitylearn.com. 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