{"id":39817,"date":"2026-07-01T16:55:41","date_gmt":"2026-07-01T14:55:41","guid":{"rendered":"https:\/\/www.swisslearn.org\/?p=39817"},"modified":"2026-07-01T17:48:42","modified_gmt":"2026-07-01T15:48:42","slug":"determiner-quun-point-appartient-a-un-plan","status":"publish","type":"post","link":"https:\/\/www.swisslearn.org\/?p=39817","title":{"rendered":"D\u00e9terminer qu’un point appartient \u00e0 un plan"},"content":{"rendered":"

Un plan est repr\u00e9sent\u00e9 par un syst\u00e8me de trois \u00e9quations. Voici un exemple :<\/p>\n

\"\left\{\begin{matrix} x=2+3k+l\\y=1+2k-l\\z=3-k+3l\end{matrix}\right.\"<\/p>\n

Les lettres k et l sont des nombres r\u00e9els. On fixant ces deux nombres on peut calculer les coordonn\u00e9es d’un point qui sera n\u00e9cessairement sur ce plan. Par exemple on fixer k = 1 et l = -3. On peut ainsi calculer un x, un y et un z:<\/p>\n

\"x=2+3∙1-3=2\"
\n\"y=1+2∙1-3=0\"
\n\"z=3-1+3∙(-3)=-7\"<\/p>\n

Le point P(2; 0; -7) est un point du plan.<\/p>\n

A l’inverse, pour un point donn\u00e9e, on peut d\u00e9terminer s’il est sur le plan en d\u00e9montrant que ses coordpnn\u00e9e sont le produit des m\u00eames param\u00e8tres.<\/p>\n","protected":false},"excerpt":{"rendered":"

Un plan est repr\u00e9sent\u00e9 par un syst\u00e8me de trois \u00e9quations. Voici un exemple : Les lettres k et l sont des nombres r\u00e9els. On fixant ces deux nombres on peut calculer les coordonn\u00e9es d’un point qui sera n\u00e9cessairement sur ce plan. Par exemple on fixer k = 1 et l = -3. On peut ainsi […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_et_pb_use_builder":"","_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":[38,66,10,58],"tags":[],"class_list":["post-39817","post","type-post","status-publish","format-standard","hentry","category-cours","category-en-cours-dedition","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":"Cours<\/a> En cours d'\u00e9dition<\/a> G\u00e9om\u00e9trie<\/a> G\u00e9om\u00e9trie de l'espace<\/a>","rttpg_excerpt":"Un plan est repr\u00e9sent\u00e9 par un syst\u00e8me de trois \u00e9quations. Voici un exemple : Les lettres k et l sont des nombres r\u00e9els. On fixant ces deux nombres on peut calculer les coordonn\u00e9es d’un point qui sera n\u00e9cessairement sur ce plan. Par exemple on fixer k = 1 et l = -3. On peut ainsi\u2026","_links":{"self":[{"href":"https:\/\/www.swisslearn.org\/index.php?rest_route=\/wp\/v2\/posts\/39817"}],"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=39817"}],"version-history":[{"count":10,"href":"https:\/\/www.swisslearn.org\/index.php?rest_route=\/wp\/v2\/posts\/39817\/revisions"}],"predecessor-version":[{"id":39838,"href":"https:\/\/www.swisslearn.org\/index.php?rest_route=\/wp\/v2\/posts\/39817\/revisions\/39838"}],"wp:attachment":[{"href":"https:\/\/www.swisslearn.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=39817"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.swisslearn.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=39817"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.swisslearn.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=39817"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}