{"id":6357,"date":"2010-12-08T21:27:30","date_gmt":"2010-12-08T21:27:30","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=6357"},"modified":"2022-01-12T14:22:45","modified_gmt":"2022-01-12T14:22:45","slug":"procure-uma-solucao-para-a-seguinte-condicao-e-apresente-uma-interpretacao-geometrica","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=6357","title":{"rendered":"Procure uma solu\u00e7\u00e3o para a seguinte condi\u00e7\u00e3o e apresente uma interpreta\u00e7\u00e3o geom\u00e9trica"},"content":{"rendered":"<p><ul id='GTTabs_ul_6357' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_6357' class='GTTabs_curr'><a  id=\"6357_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_6357' ><a  id=\"6357_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_6357'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<p>Procure uma solu\u00e7\u00e3o para a seguinte condi\u00e7\u00e3o e apresente uma interpreta\u00e7\u00e3o geom\u00e9trica para o resultado que encontrar:<\/p>\n<ol>\n<li>$\\begin{matrix} \u00a0\u00a0 2x-3y-2z=2 &amp; \\wedge\u00a0 &amp; 4x-3y+z=4 &amp; \\wedge\u00a0 &amp; 2x+12y-7z=2\u00a0 \\\\ \\end{matrix}$<\/li>\n<li>$\\begin{matrix} \u00a0\u00a0 5x+y+z=-5 &amp; \\wedge\u00a0 &amp; 2x+13y-7z=-1 &amp; \\wedge\u00a0 &amp; x-y+z=1\u00a0 \\\\ \\end{matrix}$<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_6357' onClick='GTTabs_show(1,6357)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_6357'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li>Resolvendo o sistema, vem:<br \/>\n\\[\\begin{array}{*{35}{l}} \u00a0\u00a0 \\begin{array}{*{35}{r}} \u00a0\u00a0 (-2\\times ) &amp; (-1\\times )\u00a0 \\\\ \u00a0\u00a0 (+) &amp; {}\u00a0 \\\\ \u00a0\u00a0 {} &amp; (+)\u00a0 \\\\ \\end{array}\\left\\{ \\begin{array}{*{35}{l}} \u00a0\u00a0 2x-3y-2z=2\u00a0 \\\\ \u00a0\u00a0 4x-3y+z=4\u00a0 \\\\ \u00a0\u00a0 2x+12y-7z=2\u00a0 \\\\ \\end{array} \\right. &amp; \\Leftrightarrow\u00a0 &amp; \\begin{array}{*{35}{r}} \u00a0\u00a0 {}\u00a0 \\\\ \u00a0\u00a0 (1\\times )\u00a0 \\\\ \u00a0\u00a0 (+)\u00a0 \\\\ \\end{array}\\left\\{ \\begin{array}{*{35}{l}} \u00a0\u00a0 2x-3y-2z=2\u00a0 \\\\ \u00a0\u00a0 3y+5z=0\u00a0 \\\\ \u00a0\u00a0 15y-5z=0\u00a0 \\\\ \\end{array} \\right. &amp; \\Leftrightarrow\u00a0 &amp; \\left\\{ \\begin{array}{*{35}{l}} \u00a0\u00a0 2x-3y-2z=2\u00a0 \\\\ \u00a0\u00a0 3y+5z=0\u00a0 \\\\ \u00a0\u00a0 18y=0\u00a0 \\\\ \\end{array} \\right. &amp; \\Leftrightarrow\u00a0\u00a0 \\\\ \u00a0\u00a0 {} &amp; \\Leftrightarrow\u00a0 &amp; \\left\\{ \\begin{array}{*{35}{l}} \u00a0\u00a0 x=1\u00a0 \\\\ \u00a0\u00a0 y=0\u00a0 \\\\ \u00a0\u00a0 z=0\u00a0 \\\\ \\end{array} \\right. &amp; {} &amp; {} &amp; {}\u00a0 \\\\ \\end{array}\\]<br \/>\nO sistema \u00e9 poss\u00edvel e determinado; $S=\\left\\{ (1,0,0) \\right\\}$.<br \/>\nCada equa\u00e7\u00e3o do sistema define um plano e a intersec\u00e7\u00e3o desses tr\u00eas planos \u00e9 um ponto, o ponto de coordenadas $(1,0,0)$.<br \/>\n\u00ad<\/li>\n<li>Resolvendo o sistema, vem:<br \/>\n\\[\\begin{array}{*{35}{l}} \u00a0\u00a0 \\begin{array}{*{35}{r}} \u00a0\u00a0 {} &amp; (-1\\times )\u00a0 \\\\ \u00a0\u00a0 (+) &amp; {}\u00a0 \\\\ \u00a0\u00a0 (7\\times ) &amp; (+)\u00a0 \\\\ \\end{array}\\left\\{ \\begin{array}{*{35}{l}} \u00a0\u00a0 5x+y+z=-5\u00a0 \\\\ \u00a0\u00a0 2x+13y-7z=-1\u00a0 \\\\ \u00a0\u00a0 x-y+z=1\u00a0 \\\\ \\end{array} \\right. &amp; \\Leftrightarrow\u00a0 &amp; \\begin{array}{*{35}{r}} \u00a0\u00a0 {}\u00a0 \\\\ \u00a0\u00a0 (+)\u00a0 \\\\ \u00a0\u00a0 (3\\times )\u00a0 \\\\ \\end{array}\\left\\{ \\begin{array}{*{35}{l}} \u00a0\u00a0 5x+y+z=-5\u00a0 \\\\ \u00a0\u00a0 9x+6y=6\u00a0 \\\\ \u00a0\u00a0 -4x-2y=6\u00a0 \\\\ \\end{array} \\right. &amp; \\Leftrightarrow\u00a0 &amp; \\left\\{ \\begin{array}{*{35}{l}} \u00a0\u00a0 5x+y+z=-5\u00a0 \\\\ \u00a0\u00a0 -4x-2y=6\u00a0 \\\\ \u00a0\u00a0 -3x=24\u00a0 \\\\ \\end{array} \\right. &amp; \\Leftrightarrow\u00a0\u00a0 \\\\ \u00a0\u00a0 {} &amp; \\Leftrightarrow\u00a0 &amp; \\left\\{ \\begin{array}{*{35}{l}} \u00a0\u00a0 x=-8\u00a0 \\\\ \u00a0\u00a0 y=13\u00a0 \\\\ \u00a0\u00a0 z=22\u00a0 \\\\ \\end{array} \\right. &amp; {} &amp; {} &amp; {}\u00a0 \\\\ \\end{array}\\]<br \/>\nO sistema \u00e9 poss\u00edvel e determinado; $S=\\left\\{ (-8,13,22) \\right\\}$.<br \/>\nCada equa\u00e7\u00e3o do sistema define um plano e a intersec\u00e7\u00e3o desses tr\u00eas planos \u00e9 um ponto, o ponto de coordenadas $(-8,13,22)$.<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_6357' onClick='GTTabs_show(0,6357)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Procure uma solu\u00e7\u00e3o para a seguinte condi\u00e7\u00e3o e apresente uma interpreta\u00e7\u00e3o geom\u00e9trica para o resultado que encontrar: $\\begin{matrix} \u00a0\u00a0 2x-3y-2z=2 &amp; \\wedge\u00a0 &amp; 4x-3y+z=4 &amp; \\wedge\u00a0 &amp; 2x+12y-7z=2\u00a0 \\\\ \\end{matrix}$ $\\begin{matrix}&#46;&#46;&#46;<\/p>\n","protected":false},"author":1,"featured_media":19407,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[98,97,110],"tags":[422,67,119],"series":[],"class_list":["post-6357","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-interseccao-de-planos"],"views":1964,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2010\/11\/Intersecao_de_tres_planos.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6357","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=6357"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/6357\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/19407"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=6357"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=6357"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=6357"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=6357"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}