{"id":235175,"date":"2025-06-15T02:53:25","date_gmt":"2025-06-15T02:53:25","guid":{"rendered":"https:\/\/learnexams.com\/blog\/?p=235175"},"modified":"2025-06-15T02:53:27","modified_gmt":"2025-06-15T02:53:27","slug":"draw-the-vector-c%e2%83%97-0-5a%e2%83%97-2b%e2%83%97","status":"publish","type":"post","link":"https:\/\/www.learnexams.com\/blog\/2025\/06\/15\/draw-the-vector-c%e2%83%97-0-5a%e2%83%97-2b%e2%83%97\/","title":{"rendered":"Draw the vector C\u20d7 =0.5A\u20d7 +2B\u20d7"},"content":{"rendered":"\n

Draw the vector C\u20d7 =0.5A\u20d7 +2B\u20d7 . Only the length and orientation of vector C\u20d7 will be graded. The location of the vector is not important.<\/p>\n\n\n\n

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

To draw the vector \ud835\udc36\u20d7 = 0.5\ud835\udc34\u20d7 + 2\ud835\udc35\u20d7<\/strong>, it is first necessary to understand vector addition and scalar multiplication.<\/p>\n\n\n\n

Step-by-step Explanation:<\/h3>\n\n\n\n
    \n
  1. Scalar Multiplication<\/strong>:\n
      \n
    • The vector \ud835\udc34\u20d7<\/strong> is multiplied by 0.5<\/strong>, meaning the resulting vector will have the same direction as \ud835\udc34\u20d7<\/strong> but half its magnitude.<\/li>\n\n\n\n
    • The vector \ud835\udc35\u20d7<\/strong> is multiplied by 2<\/strong>, meaning the resulting vector will have the same direction as \ud835\udc35\u20d7<\/strong>, but its magnitude will be twice as long.<\/li>\n<\/ul>\n<\/li>\n\n\n\n
    • Vector Addition<\/strong>:\n
        \n
      • To add 0.5\ud835\udc34\u20d7<\/strong> and 2\ud835\udc35\u20d7<\/strong>, place the tail of 2\ud835\udc35\u20d7<\/strong> at the head of 0.5\ud835\udc34\u20d7<\/strong>. The resultant vector \ud835\udc36\u20d7<\/strong> is drawn from the tail of 0.5\ud835\udc34\u20d7<\/strong> to the head of 2\ud835\udc35\u20d7<\/strong>.<\/li>\n<\/ul>\n<\/li>\n\n\n\n
      • Geometric Construction<\/strong>:\n
          \n
        • Draw vector 0.5\ud835\udc34\u20d7<\/strong> with correct orientation and half the original length of \ud835\udc34\u20d7<\/strong>.<\/li>\n\n\n\n
        • At the tip of 0.5\ud835\udc34\u20d7<\/strong>, draw vector 2\ud835\udc35\u20d7<\/strong>, ensuring it maintains the direction of \ud835\udc35\u20d7<\/strong>, but has twice the length.<\/li>\n\n\n\n
        • Connect the start of 0.5\ud835\udc34\u20d7<\/strong> to the end of 2\ud835\udc35\u20d7<\/strong>. This line represents \ud835\udc36\u20d7<\/strong>.<\/li>\n<\/ul>\n<\/li>\n\n\n\n
        • Length and Orientation<\/strong>:\n
            \n
          • The length of \ud835\udc36\u20d7<\/strong> depends on both the magnitude and direction of 0.5\ud835\udc34\u20d7<\/strong> and 2\ud835\udc35\u20d7<\/strong>.<\/li>\n\n\n\n
          • If \ud835\udc34\u20d7<\/strong> and \ud835\udc35\u20d7<\/strong> point in similar directions, the resulting vector will be longer and close in direction to both.<\/li>\n\n\n\n
          • If \ud835\udc34\u20d7<\/strong> and \ud835\udc35\u20d7<\/strong> point in opposite directions, their contributions may partially cancel, shortening the resulting vector and altering its direction.<\/li>\n<\/ul>\n<\/li>\n<\/ol>\n\n\n\n

            Now, based on a given diagram or orientation of \ud835\udc34\u20d7<\/strong> and \ud835\udc35\u20d7<\/strong>, the correct drawing of \ud835\udc36\u20d7<\/strong> will maintain the direction and scaled length based on the vector sum described above.<\/p>\n\n\n\n

            Please upload the diagram of \ud835\udc34\u20d7<\/strong> and \ud835\udc35\u20d7<\/strong>, or describe their directions and magnitudes, so the specific drawing of \ud835\udc36\u20d7<\/strong> can be generated accurately.<\/p>\n\n\n\n

            \"\"<\/figure>\n","protected":false},"excerpt":{"rendered":"

            Draw the vector C\u20d7 =0.5A\u20d7 +2B\u20d7 . Only the length and orientation of vector C\u20d7 will be graded. The location of the vector is not important. The Correct Answer and Explanation is: To draw the vector \ud835\udc36\u20d7 = 0.5\ud835\udc34\u20d7 + 2\ud835\udc35\u20d7, it is first necessary to understand vector addition and scalar multiplication. Step-by-step Explanation: Now, […]<\/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-235175","post","type-post","status-publish","format-standard","hentry","category-exams-certification"],"_links":{"self":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/235175","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=235175"}],"version-history":[{"count":0,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/posts\/235175\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/media?parent=235175"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/categories?post=235175"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.learnexams.com\/blog\/wp-json\/wp\/v2\/tags?post=235175"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}