{"id":5941,"date":"2010-11-22T00:21:08","date_gmt":"2010-11-22T00:21:08","guid":{"rendered":"https:\/\/www.acasinhadamatematica.pt\/?p=5941"},"modified":"2022-01-12T13:58:31","modified_gmt":"2022-01-12T13:58:31","slug":"pontos-pertencentes-a-um-plano-dado","status":"publish","type":"post","link":"https:\/\/www.acasinhadamatematica.pt\/?p=5941","title":{"rendered":"Pontos pertencentes a um plano dado"},"content":{"rendered":"<p><ul id='GTTabs_ul_5941' class='GTTabs' style='display:none'>\n<li id='GTTabs_li_0_5941' class='GTTabs_curr'><a  id=\"5941_0\" onMouseOver=\"GTTabsShowLinks('Enunciado'); return true;\"  onMouseOut=\"GTTabsShowLinks();\"  class='GTTabsLinks'>Enunciado<\/a><\/li>\n<li id='GTTabs_li_1_5941' ><a  id=\"5941_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_5941'>\n<span class='GTTabs_titles'><b>Enunciado<\/b><\/span><\/p>\n<ol>\n<li>Averigue se o ponto $A(-7,-3,-1)$ pertence ao plano de equa\u00e7\u00e3o $x-2y-3z=2$.<\/li>\n<li>Determine as coordenadas de dois pontos do plano de equa\u00e7\u00e3o $3x-y+4z=10$.<\/li>\n<\/ol>\n<p><div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_next'><a href='#GTTabs_ul_5941' onClick='GTTabs_show(1,5941)'>Resolu\u00e7\u00e3o &gt;&gt;<\/a><\/span><\/div><\/div>\n\n<div class='GTTabs_divs' id='GTTabs_1_5941'>\n<span class='GTTabs_titles'><b>Resolu\u00e7\u00e3o<\/b><\/span><!--more--><\/p>\n<ol>\n<li>Como $-7-2\\times (-3)-3\\times (-1)=2\\Leftrightarrow -7+6+3=2\\Leftrightarrow 2=2$ (P.V.), o ponto A pertence ao plano dado, pois as suas coordenadas verificam a equa\u00e7\u00e3o do plano.<br \/>\n\u00ad<\/li>\n<li>Fazendo $x=0\\wedge y=0$, vem $0-0+4z=10\\Leftrightarrow z=\\frac{5}{2}$.<br \/>\nLogo, $P(0,0,\\frac{5}{2})$ \u00e9 um ponto do plano dado.<\/p>\n<p>Fazendo $x=1\\wedge z=1$, vem $3-y+4=10\\Leftrightarrow y=-3$.<br \/>\nLogo,\u00a0$Q(1,-3,1)$ \u00e9 outro ponto do plano dado.<\/p>\n<\/li>\n<\/ol>\n<div class='GTTabsNavigation' style='display:none'><span class='GTTabs_nav_prev'><a href='#GTTabs_ul_5941' onClick='GTTabs_show(0,5941)'>&lt;&lt; Enunciado<\/a><\/span><\/div><\/div>\n\n","protected":false},"excerpt":{"rendered":"<p>Enunciado Resolu\u00e7\u00e3o Enunciado Averigue se o ponto $A(-7,-3,-1)$ pertence ao plano de equa\u00e7\u00e3o $x-2y-3z=2$. Determine as coordenadas de dois pontos do plano de equa\u00e7\u00e3o $3x-y+4z=10$. Resolu\u00e7\u00e3o &gt;&gt; Resolu\u00e7\u00e3o &lt;&lt; Enunciado<\/p>\n","protected":false},"author":1,"featured_media":19181,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[98,97,110],"tags":[422,67,117],"series":[],"class_list":["post-5941","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-plano"],"views":1583,"jetpack_featured_media_url":"https:\/\/www.acasinhadamatematica.pt\/wp-content\/uploads\/2021\/12\/Mat72.png","jetpack_sharing_enabled":true,"jetpack_likes_enabled":true,"_links":{"self":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/5941","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=5941"}],"version-history":[{"count":0,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/posts\/5941\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=\/wp\/v2\/media\/19181"}],"wp:attachment":[{"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=5941"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=5941"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=5941"},{"taxonomy":"series","embeddable":true,"href":"https:\/\/www.acasinhadamatematica.pt\/index.php?rest_route=%2Fwp%2Fv2%2Fseries&post=5941"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}