{"id":38950,"date":"2024-06-21T10:32:28","date_gmt":"2024-06-21T08:32:28","guid":{"rendered":"https:\/\/www.swisslearn.org\/?p=38950"},"modified":"2024-06-23T18:12:32","modified_gmt":"2024-06-23T16:12:32","slug":"traces-dun-plan-exemple-n-2","status":"publish","type":"post","link":"https:\/\/www.swisslearn.org\/?p=38950","title":{"rendered":"Traces d&rsquo;un plan: exemple n\u00b0 2"},"content":{"rendered":"<p><a href=\"https:\/\/www.swisslearn.org\/?p=38934\">Exemples<\/a> n\u00b0 <a href=\"https:\/\/www.swisslearn.org\/?p=38944\">1<\/a>, 2, <a href=\"https:\/\/www.swisslearn.org\/?p=38972\">3<\/a>, <a href=\"https:\/\/www.swisslearn.org\/?p=38975\">4<\/a>, <a href=\"https:\/\/www.swisslearn.org\/?p=38980\">5<\/a>, <a href=\"https:\/\/www.swisslearn.org\/?p=38983\">6<\/a><br \/>\n<iframe loading=\"lazy\" style=\"border: 0px;\" src=\"https:\/\/www.geogebra.org\/material\/iframe\/id\/ypwzpfs7\/width\/1200\/height\/715\/border\/888888\/rc\/true\/ai\/false\/sdz\/true\/smb\/false\/stb\/false\/stbh\/true\/ld\/false\/sri\/false\/sfsb\/true\" width=\"1600px\" height=\"715px\" scrolling=\"no\" allowfullscreen=\"allowfullscreen\" data-mce-fragment=\"1\">Explications<\/p>\n<p><\/iframe><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\alpha&amp;space;:\\left\\{\\begin{matrix}&amp;space;x=8+2k+6l&amp;space;\\\\&amp;space;y=-1-k&amp;space;\\\\&amp;space;z=5l&amp;space;\\end{matrix}\\right.\" alt=\"\\alpha :\\left\\{\\begin{matrix} x=8+2k+6l \\\\ y=-1-k \\\\ z=5l \\end{matrix}\\right.\" align=\"absmiddle\" \/><\/p>\n<p>Pour dessiner les traces du plan <em>\u03b1<\/em> il faut d\u00e9terminer les points d&rsquo;intersection de ce plan avec les trois axes du rep\u00e8re.<\/p>\n<p><strong>Point A, intersection du plan <em>\u03b1<\/em> avec l&rsquo;axe <em>Ox<\/em> (y = 0 et z = 0)<\/strong><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?A&amp;space;\\in&amp;space;Ox&amp;space;\\Rightarrow\" alt=\"A \\in Ox \\Rightarrow\" align=\"absmiddle\" \/><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?y=0&amp;space;\\Rightarrow&amp;space;-1-k=0\\Rightarrow&amp;space;k=-1\" alt=\"y=0 \\Rightarrow -1-k=0\\Rightarrow k=-1\" align=\"absmiddle\" \/><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?z=0\\Rightarrow&amp;space;5l=0\\Rightarrow&amp;space;l=0\" alt=\"z=0\\Rightarrow 5l=0\\Rightarrow l=0\" align=\"absmiddle\" \/><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\Rightarrow&amp;space;x=8+2(-1)+6\\cdot&amp;space;0&amp;space;=6\" alt=\"\\Rightarrow x=8+2(-1)+6\\cdot 0 =6\" align=\"absmiddle\" \/><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?A(6;&amp;space;0;&amp;space;0)\" alt=\"A(6; 0; 0)\" align=\"absmiddle\" \/><\/p>\n<p><strong>Point B, intersection du plan <em>\u03b1<\/em> avec l&rsquo;axe <em>Oy<\/em> (x = 0 et z = 0)<\/strong><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?B\\in&amp;space;Oy&amp;space;\\Rightarrow\" alt=\"B\\in Oy \\Rightarrow\" align=\"absmiddle\" \/><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?x=0&amp;space;\\Rightarrow&amp;space;8+2k+6l=0\" alt=\"x=0 \\Rightarrow 8+2k+6l=0\" align=\"absmiddle\" \/><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?z=0\\Rightarrow&amp;space;5l=0\\Rightarrow&amp;space;l=0\" alt=\"z=0\\Rightarrow 5l=0\\Rightarrow l=0\" align=\"absmiddle\" \/> <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\Rightarrow&amp;space;8+2k+6\\cdot&amp;space;0=0\\Rightarrow&amp;space;2k=-8\\Rightarrow&amp;space;k=-4\" alt=\"\\Rightarrow 8+2k+6\\cdot 0=0\\Rightarrow 2k=-8\\Rightarrow k=-4\" align=\"absmiddle\" \/><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\Rightarrow&amp;space;y=-1-(-4)&amp;space;=3\" alt=\"\\Rightarrow y=-1-(-4) =3\" align=\"absmiddle\" \/><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?B(0;&amp;space;3;&amp;space;0)\" alt=\"B(0; 3; 0)\" align=\"absmiddle\" \/><\/p>\n<p><strong>Point C, intersection du plan <em>\u03b1<\/em> avec l&rsquo;axe <em>Oz<\/em> (x = 0 et y = 0)<\/strong><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?C\\in&amp;space;Oz&amp;space;\\Rightarrow\" alt=\"C\\in Oz \\Rightarrow\" align=\"absmiddle\" \/><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?x=0&amp;space;\\Rightarrow&amp;space;8+2k+6l=0\" alt=\"x=0 \\Rightarrow 8+2k+6l=0\" align=\"absmiddle\" \/><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?y=0\\Rightarrow&amp;space;-1-k=0\\Rightarrow&amp;space;k=-1\" alt=\"y=0\\Rightarrow -1-k=0\\Rightarrow k=-1\" align=\"absmiddle\" \/> <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\Rightarrow&amp;space;8+2(-1)+6l=0\\Rightarrow&amp;space;6l=-6\\Rightarrow&amp;space;l=-1\" alt=\"\\Rightarrow 8+2(-1)+6l=0\\Rightarrow 6l=-6\\Rightarrow l=-1\" align=\"absmiddle\" \/><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\Rightarrow&amp;space;z=5(-1)=-5\" alt=\"\\Rightarrow z=5(-1)=-5\" align=\"absmiddle\" \/><\/p>\n<p><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?C(0;&amp;space;0;&amp;space;-5)\" alt=\"C(0; 0; -5)\" align=\"absmiddle\" \/><\/p>\n<p>Le plan <em>\u03b1<\/em> coupe les trois axes du rep\u00e8re aux points A, B et C. Les parties visibles des des droites passant par A et B(trace sur le sol ou <em>\u03b1&rsquo;<\/em>), de la droite passant par B et C (sur le mur ou <img loading=\"lazy\" decoding=\"async\" class=\"alignnone\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\inline&amp;space;\\small&amp;space;\\alpha''\" alt=\"\\inline \\small \\alpha''\" width=\"18\" height=\"11\" align=\"absmiddle\" \/>) et de la droite passant par A et C (trace sur la paroi our <img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\inline&amp;space;\\small&amp;space;\\alpha'''\" alt=\"\\inline \\small \\alpha'''\" align=\"absmiddle\" \/>) constituent les traces du plan <em>\u03b1<\/em>. Notez que la cote (z) du point C est n\u00e9gative. Ce point ne fait pas partie de la partie visible du plan <em>\u03b1.<\/em><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Exemples n\u00b0 1, 2, 3, 4, 5, 6 Explications Pour dessiner les traces du plan \u03b1 il faut d\u00e9terminer les points d&rsquo;intersection de ce plan avec les trois axes du rep\u00e8re. Point A, intersection du plan \u03b1 avec l&rsquo;axe Ox (y = 0 et z = 0) Point B, intersection du plan \u03b1 avec l&rsquo;axe [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_et_pb_use_builder":"off","_et_pb_old_content":"","_et_gb_content_width":"","_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"categories":[10,58],"tags":[],"class_list":["post-38950","post","type-post","status-publish","format-standard","hentry","category-geometrie","category-geometrie-de-lespace"],"blocksy_meta":"","rttpg_featured_image_url":null,"rttpg_author":{"display_name":"Bahram Zaerpour","author_link":"https:\/\/www.swisslearn.org\/?author=1"},"rttpg_comment":0,"rttpg_category":"<a href=\"https:\/\/www.swisslearn.org\/?cat=10\" rel=\"category\">G\u00e9om\u00e9trie<\/a> <a href=\"https:\/\/www.swisslearn.org\/?cat=58\" rel=\"category\">G\u00e9om\u00e9trie de l'espace<\/a>","rttpg_excerpt":"Exemples n\u00b0 1, 2, 3, 4, 5, 6 Explications Pour dessiner les traces du plan \u03b1 il faut d\u00e9terminer les points d&rsquo;intersection de ce plan avec les trois axes du rep\u00e8re. Point A, intersection du plan \u03b1 avec l&rsquo;axe Ox (y = 0 et z = 0) Point B, intersection du plan \u03b1 avec l&rsquo;axe\u2026","_links":{"self":[{"href":"https:\/\/www.swisslearn.org\/index.php?rest_route=\/wp\/v2\/posts\/38950"}],"collection":[{"href":"https:\/\/www.swisslearn.org\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.swisslearn.org\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.swisslearn.org\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.swisslearn.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=38950"}],"version-history":[{"count":5,"href":"https:\/\/www.swisslearn.org\/index.php?rest_route=\/wp\/v2\/posts\/38950\/revisions"}],"predecessor-version":[{"id":39018,"href":"https:\/\/www.swisslearn.org\/index.php?rest_route=\/wp\/v2\/posts\/38950\/revisions\/39018"}],"wp:attachment":[{"href":"https:\/\/www.swisslearn.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=38950"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.swisslearn.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=38950"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.swisslearn.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=38950"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}