{"id":6373,"date":"2010-12-13T18:34:16","date_gmt":"2010-12-13T18:34:16","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=6373"},"modified":"2022-01-21T22:08:17","modified_gmt":"2022-01-21T22:08:17","slug":"abcdefgh-e-um-cubo","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=6373","title":{"rendered":"[ABCDEFGH] \u00e9 um cubo"},"content":{"rendered":"<p><ul id='GTTabs_ul_6373' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_6373' class='GTTabs_curr'><a  id=\"6373_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_6373' ><a  id=\"6373_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_6373'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p><a href=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/12\/pag185-48.jpg\"><img loading=\"lazy\" decoding=\"async\" data-attachment-id=\"6374\" data-permalink=\"https:\/\/www.acasinhadamatematica.pt\/?attachment_id=6374\" data-orig-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/12\/pag185-48.jpg\" data-orig-size=\"298,297\" data-comments-opened=\"1\" data-image-meta=\"{&quot;aperture&quot;:&quot;0&quot;,&quot;credit&quot;:&quot;&quot;,&quot;camera&quot;:&quot;HP pstc4380&quot;,&quot;caption&quot;:&quot;&quot;,&quot;created_timestamp&quot;:&quot;0&quot;,&quot;copyright&quot;:&quot;&quot;,&quot;focal_length&quot;:&quot;0&quot;,&quot;iso&quot;:&quot;0&quot;,&quot;shutter_speed&quot;:&quot;0&quot;,&quot;title&quot;:&quot;&quot;}\" data-image-title=\"Cubo\" data-image-description=\"\" data-image-caption=\"\" data-large-file=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/12\/pag185-48.jpg\" class=\"alignright size-full wp-image-6374\" title=\"Cubo\" src=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/12\/pag185-48.jpg\" alt=\"\" width=\"143\" height=\"142\" srcset=\"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/12\/pag185-48.jpg 298w, https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/12\/pag185-48-150x150.jpg 150w\" sizes=\"auto, (max-width: 143px) 100vw, 143px\" \/><\/a>[ABCDEFGH] \u00e9 um cubo.<\/p>\n<p>Os pontos A, E, F e H t\u00eam por coordenadas, respetivamente, $(1,1,3)$, $(1,1,1)$, $(1,3,1)$ e $(-1,1,1)$.<\/p>\n<ol>\n<li>Calcule as coordenadas dos restantes v\u00e9rtices.<\/li>\n<li>Escreva uma equa\u00e7\u00e3o do plano AEC.<\/li>\n<li>Escreva equa\u00e7\u00f5es cartesianas das retas BF e EC.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_6373' onClick='GTTabs_show(1,6373)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_6373'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li><span class=\"alignright\"><script src=\"http:\/\/tube.geogebra.org\/scripts\/deployggb.js\"><\/script>\r\n<body>\r\n<div id=\"ggbApplet\"><\/div>\r\n<script>\r\nvar parameters = {\r\n\"id\": \"ggbApplet\",\r\n\"width\":261,\r\n\"height\":213,\r\n\"showMenuBar\":false,\r\n\"showAlgebraInput\":false,\r\n\"showToolBar\":false,\r\n\"customToolBar\":\"0 39 | 1 501 67 , 5 19 , 72 | 2 15 45 , 18 65 , 7 37 | 4 3 8 9 , 13 44 , 58 , 47 | 16 51 64 , 70 | 10 34 53 11 , 24  20 22 , 21 23 | 55 56 57 , 12 | 36 46 , 38 49  50 , 71 | 30 29 54 32 31 33 | 17 26 62 73 , 14 68 | 25 52 60 61 | 40 41 42 , 27 28 35 , 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\"};\r\n\/\/ is3D=is 3D applet using 3D view, AV=Algebra View, SV=Spreadsheet View, CV=CAS View, EV2=Graphics View 2, CP=Construction Protocol, PC=Probability Calculator, DA=Data Analysis, FI=Function Inspector, PV=Python, macro=Macro View\r\nvar views = {'is3D': 0,'AV': 0,'SV': 0,'CV': 0,'EV2': 0,'CP': 0,'PC': 0,'DA': 0,'FI': 0,'PV': 0,'macro': 0};\r\nvar applet = new GGBApplet(parameters, '5.0', views);\r\nwindow.onload = function() {applet.inject('ggbApplet')};\r\n<\/script><\/span>As coordenadas dos restantes v\u00e9rtices s\u00e3o: $B\\,(1,3,3)$, $C\\,(-1,3,3)$, $D\\,(-1,1,3)$ e $G\\,(-1,3,1)$.<br \/>\n\u00ad<\/li>\n<li>Um vector normal ao plano AEC \u00e9, por exemplo, o vetor $\\overrightarrow{DB}=(2,2,0)$.<br \/>\nLogo, a equa\u00e7\u00e3o do plano AEC \u00e9 da forma $2x+2y+d=0$.<\/p>\n<p>Dado que o ponto $A\\,(1,1,3)$ pertence a esse plano, as suas coordenadas t\u00eam de verificar esta equa\u00e7\u00e3o. Assim, $2\\times 1+2\\times 1+d=0\\Leftrightarrow d=-4$.<\/p>\n<p>Logo, $x+y-2=0$ \u00e9 uma equa\u00e7\u00e3o do plano AEC.<br \/>\n\u00ad<\/p>\n<\/li>\n<li>A reta BF pode ser definida por $x=1\\wedge y=3$. (Porqu\u00ea?)\n<p>Quanto \u00e0 reta EC, sendo $E\\,(1,1,1)$ e $\\overrightarrow{EC}=(-2,2,2)$, podemos defini-la da seguinte forma:<br \/>\n\\[\\frac{x-1}{-2}=\\frac{y-1}{2}=\\frac{z-1}{2}\\Leftrightarrow -x+1=y-1=z-1\\Leftrightarrow x+y-2=0\\wedge y-z=0\\]<\/p>\n<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_6373' onClick='GTTabs_show(0,6373)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado [ABCDEFGH] \u00e9 um cubo. Os pontos A, E, F e H t\u00eam por coordenadas, respetivamente, $(1,1,3)$, $(1,1,1)$, $(1,3,1)$ e $(-1,1,1)$. Calcule as coordenadas dos restantes v\u00e9rtices. Escreva uma equa\u00e7\u00e3o do plano&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":20835,"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],"series":[],"class_list":["post-6373","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"],"views":1982,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/12\/11V1Pag185-48_520x245.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6373","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=6373"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6373\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/20835"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=6373"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=6373"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=6373"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=6373"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}