{"id":27197,"date":"2025-06-19T21:29:51","date_gmt":"2025-06-19T21:29:51","guid":{"rendered":"https:\/\/gaviki.com\/blog\/?p=27197"},"modified":"2025-06-19T21:29:53","modified_gmt":"2025-06-19T21:29:53","slug":"the-three-displacement-vectors-in-the-drawing-have-magnitudes-of","status":"publish","type":"post","link":"https:\/\/gaviki.com\/blog\/the-three-displacement-vectors-in-the-drawing-have-magnitudes-of\/","title":{"rendered":"The three displacement vectors in the drawing have magnitudes of"},"content":{"rendered":"\n<p>The three displacement vectors in the drawing have magnitudes of A= 5.00 m B= 5.00 m and C= 4.00 m. Find the resultant( magnitude and directional angle) of three vectors by mean of the component method. express the directional angle as an angle above the positive or negative x-axis<\/p>\n\n\n\n<p><strong><mark style=\"background-color:rgba(0, 0, 0, 0)\" class=\"has-inline-color has-vivid-red-color\">The Correct Answer and Explanation is:<\/mark><\/strong><\/p>\n\n\n\n<p>To find the <strong>resultant displacement vector<\/strong> of three given vectors <strong>A<\/strong>, <strong>B<\/strong>, and <strong>C<\/strong>, using the <strong>component method<\/strong>, we follow these steps:<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Step 1: Understand the vectors and their directions<\/strong><\/h3>\n\n\n\n<p>Assume the vectors are oriented as follows (a common setup unless stated otherwise):<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Vector <strong>A<\/strong> is along the <strong>positive x-axis<\/strong><\/li>\n\n\n\n<li>Vector <strong>B<\/strong> is at a <strong>45\u00b0 angle above the positive x-axis<\/strong><\/li>\n\n\n\n<li>Vector <strong>C<\/strong> is along the <strong>negative y-axis<\/strong><\/li>\n<\/ul>\n\n\n\n<p>Given:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>A = 5.00 m<\/li>\n\n\n\n<li>B = 5.00 m<\/li>\n\n\n\n<li>C = 4.00 m<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Step 2: Break each vector into components<\/strong><\/h3>\n\n\n\n<p><strong>Vector A:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Ax = 5.00 m<\/li>\n\n\n\n<li>Ay = 0.00 m<\/li>\n<\/ul>\n\n\n\n<p><strong>Vector B:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Bx = B \u00d7 cos(45\u00b0) = 5.00 \u00d7 0.7071 \u2248 3.54 m<\/li>\n\n\n\n<li>By = B \u00d7 sin(45\u00b0) = 5.00 \u00d7 0.7071 \u2248 3.54 m<\/li>\n<\/ul>\n\n\n\n<p><strong>Vector C:<\/strong><\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Cx = 0.00 m<\/li>\n\n\n\n<li>Cy = \u20134.00 m (since it is directed downward)<\/li>\n<\/ul>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Step 3: Add components<\/strong><\/h3>\n\n\n\n<p><strong>Total x-component (Rx):<\/strong><br>Rx = Ax + Bx + Cx<br>Rx = 5.00 + 3.54 + 0.00 = <strong>8.54 m<\/strong><\/p>\n\n\n\n<p><strong>Total y-component (Ry):<\/strong><br>Ry = Ay + By + Cy<br>Ry = 0.00 + 3.54 \u2013 4.00 = <strong>\u20130.46 m<\/strong><\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Step 4: Find magnitude of the resultant vector<\/strong><\/h3>\n\n\n\n<p>R=(Rx)2+(Ry)2=(8.54)2+(\u22120.46)2\u224872.96+0.21\u224873.17\u22488.56&nbsp;mR = \\sqrt{(Rx)^2 + (Ry)^2} = \\sqrt{(8.54)^2 + (-0.46)^2} \\approx \\sqrt{72.96 + 0.21} \\approx \\sqrt{73.17} \\approx 8.56\\ \\text{m}R=(Rx)2+(Ry)2\u200b=(8.54)2+(\u22120.46)2\u200b\u224872.96+0.21\u200b\u224873.17\u200b\u22488.56&nbsp;m<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Step 5: Find the directional angle<\/strong><\/h3>\n\n\n\n<p>\u03b8=tan\u2061\u22121(RyRx)=tan\u2061\u22121(\u22120.468.54)\u2248tan\u2061\u22121(\u22120.0539)\u2248\u22123.1\u2218\\theta = \\tan^{-1}\\left(\\frac{Ry}{Rx}\\right) = \\tan^{-1}\\left(\\frac{-0.46}{8.54}\\right) \\approx \\tan^{-1}(-0.0539) \\approx -3.1^\\circ\u03b8=tan\u22121(RxRy\u200b)=tan\u22121(8.54\u22120.46\u200b)\u2248tan\u22121(\u22120.0539)\u2248\u22123.1\u2218<\/p>\n\n\n\n<p>Since Rx is positive and Ry is negative, the vector lies slightly <strong>below the positive x-axis<\/strong>.<\/p>\n\n\n\n<hr class=\"wp-block-separator has-alpha-channel-opacity\"\/>\n\n\n\n<h3 class=\"wp-block-heading\"><strong>Final Answer:<\/strong><\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li><strong>Magnitude<\/strong> = <strong>8.56 m<\/strong><\/li>\n\n\n\n<li><strong>Direction<\/strong> = <strong>3.1\u00b0 below the positive x-axis<\/strong><\/li>\n<\/ul>\n\n\n\n<p>Or equivalently:<br><strong>Angle = 356.9\u00b0 measured counterclockwise from the positive x-axis<\/strong><\/p>\n\n\n\n<figure class=\"wp-block-image size-full\"><img loading=\"lazy\" decoding=\"async\" width=\"852\" height=\"1024\" src=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-150.jpeg\" alt=\"\" class=\"wp-image-27204\" srcset=\"https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-150.jpeg 852w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-150-250x300.jpeg 250w, https:\/\/gaviki.com\/blog\/wp-content\/uploads\/2025\/06\/learnexams-banner8-150-768x923.jpeg 768w\" sizes=\"auto, (max-width: 852px) 100vw, 852px\" \/><\/figure>\n","protected":false},"excerpt":{"rendered":"<p>The three displacement vectors in the drawing have magnitudes of A= 5.00 m B= 5.00 m and C= 4.00 m. Find the resultant( magnitude and directional angle) of three vectors by mean of the component method. express the directional angle as an angle above the positive or negative x-axis The Correct Answer and Explanation is: [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[1],"tags":[],"class_list":["post-27197","post","type-post","status-publish","format-standard","hentry","category-quiz-questions"],"_links":{"self":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/27197","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/comments?post=27197"}],"version-history":[{"count":1,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/27197\/revisions"}],"predecessor-version":[{"id":27205,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/posts\/27197\/revisions\/27205"}],"wp:attachment":[{"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/media?parent=27197"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/categories?post=27197"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/gaviki.com\/blog\/wp-json\/wp\/v2\/tags?post=27197"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}