{"id":183899,"date":"2025-01-17T08:27:13","date_gmt":"2025-01-17T08:27:13","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=183899"},"modified":"2025-01-17T08:27:14","modified_gmt":"2025-01-17T08:27:14","slug":"three-displacement-vectors-have-lengths-1-m-2-m-and-4-m","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/01\/17\/three-displacement-vectors-have-lengths-1-m-2-m-and-4-m\/","title":{"rendered":"Three displacement vectors have lengths 1 m, 2 m, and 4 m"},"content":{"rendered":"\n

Three displacement vectors have lengths 1 m, 2 m, and 4 m. Could they possibly add together to get a vector of length zero?<\/p>\n\n\n\n

The Correct Answer and Explanation is :<\/strong><\/mark><\/p>\n\n\n\n

No, the three displacement vectors of lengths 1 m, 2 m, and 4 m cannot add together to result in a vector of length zero.<\/p>\n\n\n\n

Explanation:<\/h3>\n\n\n\n

To understand why, consider the conditions required for three vectors to sum to zero. The vectors must form a closed triangle because, geometrically, a closed triangle ensures that the sum of the vectors is zero (the head of the last vector meets the tail of the first vector).<\/p>\n\n\n\n

Triangle Inequality Theorem:<\/h4>\n\n\n\n

For three vectors to form a triangle:<\/p>\n\n\n\n

    \n
  1. The sum of the lengths of any two sides must be greater than or equal to the length of the third side.<\/li>\n\n\n\n
  2. Mathematically:\n
      \n
    • a+b\u2265ca + b \\geq c<\/li>\n\n\n\n
    • b+c\u2265ab + c \\geq a<\/li>\n\n\n\n
    • c+a\u2265bc + a \\geq b<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n

      For the given vectors of lengths 1 m, 2 m, and 4 m:<\/p>\n\n\n\n

        \n
      1. Check 1+2\u226541 + 2 \\geq 4: False<\/strong> (1 + 2 = 3, which is less than 4).<\/li>\n\n\n\n
      2. Check 2+4\u226512 + 4 \\geq 1: True<\/strong> (2 + 4 = 6, which is greater than 1).<\/li>\n\n\n\n
      3. Check 4+1\u226524 + 1 \\geq 2: True<\/strong> (4 + 1 = 5, which is greater than 2).<\/li>\n<\/ol>\n\n\n\n

        Since the first condition (1+2\u226541 + 2 \\geq 4) fails, the three vectors cannot form a triangle. As a result, they cannot sum to zero.<\/p>\n\n\n\n

        Intuition:<\/h4>\n\n\n\n

        When trying to add these vectors head-to-tail, the longest vector (4 m) cannot be balanced by the combined lengths of the other two vectors (1 m and 2 m). The inability to form a closed loop means the resultant vector cannot be zero.<\/p>\n\n\n\n

        Thus, it is geometrically and mathematically impossible for these vectors to sum to zero.<\/p>\n","protected":false},"excerpt":{"rendered":"

        Three displacement vectors have lengths 1 m, 2 m, and 4 m. Could they possibly add together to get a vector of length zero? The Correct Answer and Explanation is : No, the three displacement vectors of lengths 1 m, 2 m, and 4 m cannot add together to result in a vector of length […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","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":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[25],"tags":[],"class_list":["post-183899","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/183899","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/comments?post=183899"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/183899\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=183899"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=183899"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=183899"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}