{"id":250326,"date":"2025-07-10T08:54:26","date_gmt":"2025-07-10T08:54:26","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=250326"},"modified":"2025-07-10T08:54:28","modified_gmt":"2025-07-10T08:54:28","slug":"for-the-pair-of-vectors-shown-on-the-right-find-components-of-the-resultant-vector-along-with-the-magnitude-and-direction-angle-of-the-resultant","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/07\/10\/for-the-pair-of-vectors-shown-on-the-right-find-components-of-the-resultant-vector-along-with-the-magnitude-and-direction-angle-of-the-resultant\/","title":{"rendered":"For the pair of vectors shown on the right; find components of the resultant vector along with the magnitude and direction angle of the resultant"},"content":{"rendered":"\n

For the pair of vectors shown on the right; find components of the resultant vector along with the magnitude and direction angle of the resultant R=v+ “-D What is the magnitude? IRI (Round to the nearest hundredth ) What is the direction angle? CR (Round to the nearest tenth as needed )<\/p>\n\n\n\n

\"\"<\/figure>\n\n\n\n

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

Here are the final answers:<\/p>\n\n\n\n

v<\/strong> = 3<\/strong> i + 6<\/strong> j
u<\/strong> = 7<\/strong> i + 3<\/strong> j<\/p>\n\n\n\n

R<\/strong> = v<\/strong> + u<\/strong> = 10<\/strong> i + 9<\/strong> j<\/p>\n\n\n\n

What is the magnitude? |R<\/strong>| = 13.45<\/strong>
(Round to the nearest hundredth.)<\/p>\n\n\n\n

What is the direction angle? \u03b8_R = 42.0<\/strong> \u00b0
(Round to the nearest tenth as needed.)<\/p>\n\n\n\n

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

This problem requires us to determine the properties of a resultant vector, which is the sum of two other vectors shown on a graph. The process involves three main steps: identifying the components of the initial vectors, calculating the components of their sum, and then finding the magnitude and direction of that sum.<\/p>\n\n\n\n

1. Finding the Components of v and u<\/strong><\/p>\n\n\n\n

First, we determine the components of vectors v<\/strong> (the red vector) and u<\/strong> (the blue vector) from the provided graph. A vector in the form xi + yj has a horizontal component x and a vertical component y. By observing the graph, we can see that both vectors start at the origin (0, 0).<\/p>\n\n\n\n

    \n
  • For vector\u00a0v<\/strong>, its tip is at the coordinate (3, 6). This means it extends 3 units along the x-axis and 6 units along the y-axis. Therefore,\u00a0v<\/strong>\u00a0= 3i + 6j.<\/li>\n\n\n\n
  • For vector\u00a0u<\/strong>, its tip is at the coordinate (7, 3). This means it extends 7 units along the x-axis and 3 units along the y-axis. Therefore,\u00a0u<\/strong>\u00a0= 7i + 3j.<\/li>\n<\/ul>\n\n\n\n

    2. Calculating the Resultant Vector R<\/strong><\/p>\n\n\n\n

    The resultant vector R<\/strong> is the sum of v<\/strong> and u<\/strong>. To add vectors, we simply add their corresponding components.<\/p>\n\n\n\n

      \n
    • R<\/strong>\u00a0=\u00a0v<\/strong>\u00a0+\u00a0u<\/strong>\u00a0= (3i + 6j) + (7i + 3j)<\/li>\n\n\n\n
    • R<\/strong>\u00a0= (3 + 7)i + (6 + 3)j<\/li>\n\n\n\n
    • R<\/strong>\u00a0= 10i + 9j<\/li>\n<\/ul>\n\n\n\n

      3. Calculating the Magnitude and Direction of R<\/strong><\/p>\n\n\n\n

      Now that we have the components of R<\/strong> (Rx = 10, Ry = 9), we can find its magnitude and direction angle.<\/p>\n\n\n\n

        \n
      • Magnitude:<\/strong>\u00a0The magnitude |R<\/strong>| is calculated using the Pythagorean theorem: |R<\/strong>| = \u221a(Rx\u00b2 + Ry\u00b2).\n
          \n
        • |R<\/strong>| = \u221a(10\u00b2 + 9\u00b2) = \u221a(100 + 81) = \u221a181<\/li>\n\n\n\n
        • |R<\/strong>| \u2248 13.4536. Rounded to the nearest hundredth, the magnitude is 13.45.<\/li>\n<\/ul>\n<\/li>\n\n\n\n
        • Direction Angle:<\/strong>\u00a0The direction angle \u03b8_R is found using the arctangent function: \u03b8_R = arctan(Ry \/ Rx).\n
            \n
          • \u03b8_R = arctan(9 \/ 10) = arctan(0.9)<\/li>\n\n\n\n
          • \u03b8_R \u2248 41.987\u00b0. Since both components are positive, the vector is in the first quadrant. Rounded to the nearest tenth, the direction angle is 42.0\u00b0.<\/li>\n<\/ul>\n<\/li>\n<\/ul>\n\n\n\n
            \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

            For the pair of vectors shown on the right; find components of the resultant vector along with the magnitude and direction angle of the resultant R=v+ “-D What is the magnitude? IRI (Round to the nearest hundredth ) What is the direction angle? CR (Round to the nearest tenth as needed ) The Correct Answer […]<\/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-250326","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/250326","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=250326"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/250326\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=250326"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=250326"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=250326"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}