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
$x=2+3\u22191-3=2$
\n$y=1+2\u22191-3=0$
\n$z=3-1+3\u2219(-3)=-7$<\/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 : $\\left\\{\\begin{matrix} x=2+3k+l\\\\y=1+2k-l\\\\z=3-k+3l\\end{matrix}\\right.$ 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 […]<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"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"],"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 : $\\left\\{\\begin{matrix} x=2+3k+l\\\\y=1+2k-l\\\\z=3-k+3l\\end{matrix}\\right.$ 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\u2026","_links":{"self":[{"href":"https:\/\/www.swisslearn.org\/index.php?rest_route=\/wp\/v2\/posts\/39817","targetHints":{"allow":["GET"]}}],"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}]}}