{"id":5282,"date":"2010-11-13T00:50:11","date_gmt":"2010-11-13T00:50:11","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=5282"},"modified":"2022-01-12T01:29:05","modified_gmt":"2022-01-12T01:29:05","slug":"outros-dois-vectores","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=5282","title":{"rendered":"Outros dois vetores"},"content":{"rendered":"<p><ul id='GTTabs_ul_5282' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_5282' class='GTTabs_curr'><a  id=\"5282_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_5282' ><a  id=\"5282_1\" onMouseOver=\"GTTabsShowLinks('Resolu\u00e7\u00e3o'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Resolu\u00e7\u00e3o<\/a><\/li>\n<\/ul>\n\n<div class='GTTabs_divs GTTabs_curr_div' id='GTTabs_0_5282'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Sendo $\\overrightarrow{u}$ e $\\overrightarrow{v}$ dois vetores, tais que $\\left\\| \\overrightarrow{u} \\right\\|=2$, $\\left\\| \\overrightarrow{v} \\right\\|=3$ e $\\overrightarrow{u}.\\overrightarrow{v}=4$, calcule:<\/p>\n<ol>\n<li>$(2\\overrightarrow{u}-\\overrightarrow{v}).(\\overrightarrow{u}+\\overrightarrow{v})$<\/li>\n<li>${{(2\\overrightarrow{u}+5\\overrightarrow{v})}^{2}}$<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_5282' onClick='GTTabs_show(1,5282)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_5282'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li>Ora, vem sucessivamente:<br \/>\n$\\begin{array}{*{35}{l}}<br \/>\n(2\\overrightarrow{u}-\\overrightarrow{v}).(\\overrightarrow{u}+\\overrightarrow{v}) &amp; = &amp; 2\\overrightarrow{u}.\\overrightarrow{u}+2\\overrightarrow{u}.\\overrightarrow{v}-\\overrightarrow{u}.\\overrightarrow{v}-\\overrightarrow{v}.\\overrightarrow{v}\u00a0 \\\\<br \/>\n{} &amp; = &amp; 2\\times 2\\times 2\\times 1+2\\times 4-4-3\\times 3\\times 1\u00a0 \\\\<br \/>\n{} &amp; = &amp; 8+8-4-9\u00a0 \\\\<br \/>\n{} &amp; = &amp; 3\u00a0 \\\\<br \/>\n\\end{array}$<br \/>\n\u00ad<\/li>\n<li>Ora, vem sucessivamente:<br \/>\n$\\begin{array}{*{35}{l}}<br \/>\n{{(2\\overrightarrow{u}+5\\overrightarrow{v})}^{2}} &amp; = &amp; 4\\overrightarrow{u}.\\overrightarrow{u}+20\\overrightarrow{u}.\\overrightarrow{v}+25\\overrightarrow{v}.\\overrightarrow{v}\u00a0 \\\\<br \/>\n{} &amp; = &amp; 4\\times 2\\times 2\\times 1+20\\times 4+25\\times 3\\times 3\\times 1\u00a0 \\\\<br \/>\n{} &amp; = &amp; 16+80+225\u00a0 \\\\<br \/>\n{} &amp; = &amp; 321\u00a0 \\\\<br \/>\n\\end{array}$<\/li>\n<\/ol>\n<blockquote>\n<p>Tenha presente a defini\u00e7\u00e3o de produto escalar de dois vetores: $\\overrightarrow{u}.\\overrightarrow{v}=\\left\\| \\overrightarrow{u} \\right\\|.\\left\\| \\overrightarrow{v} \\right\\|.\\cos (\\widehat{\\overrightarrow{u}\\,\\overrightarrow{v}})$.<\/p>\n<\/blockquote>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_5282' onClick='GTTabs_show(0,5282)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Sendo $\\overrightarrow{u}$ e $\\overrightarrow{v}$ dois vetores, tais que $\\left\\| \\overrightarrow{u} \\right\\|=2$, $\\left\\| \\overrightarrow{v} \\right\\|=3$ e $\\overrightarrow{u}.\\overrightarrow{v}=4$, calcule: $(2\\overrightarrow{u}-\\overrightarrow{v}).(\\overrightarrow{u}+\\overrightarrow{v})$ ${{(2\\overrightarrow{u}+5\\overrightarrow{v})}^{2}}$ Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Enunciado<\/p>\n","protected":false},"author":1,"featured_media":14114,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[98,97,110],"tags":[422,67,111],"series":[],"class_list":["post-5282","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-11--ano","category-aplicando","category-geometria-analitica","tag-11-o-ano","tag-geometria","tag-vectores"],"views":1884,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2018\/03\/Mat56.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/5282","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=5282"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/5282\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/14114"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=5282"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=5282"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=5282"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=5282"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}