{"id":39141,"date":"2024-06-27T11:19:37","date_gmt":"2024-06-27T09:19:37","guid":{"rendered":"https:\/\/www.swisslearn.org\/?p=39141"},"modified":"2024-06-28T09:03:16","modified_gmt":"2024-06-28T07:03:16","slug":"representation-vectorielle-dune-droite-en-3d-exemples","status":"publish","type":"post","link":"https:\/\/www.swisslearn.org\/?p=39141","title":{"rendered":"Repr\u00e9sentation vectorielle d&rsquo;une droite en 3D :  exemples"},"content":{"rendered":"<p>La repr\u00e9sentation vectorielle ou param\u00e9trique d&rsquo;une droite dans l&rsquo;espace est de type :<\/p>\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\left\\{\\begin{matrix}&amp;space;x=x_0+kx_v&amp;space;\\\\&amp;space;y=y_0+ky_v&amp;space;\\\\&amp;space;z=z_0+kz_v&amp;space;\\end{matrix}\\right.\" alt=\"\\left\\{\\begin{matrix} x=x_0+kx_v \\\\ y=y_0+ky_v \\\\ z=z_0+kz_v \\end{matrix}\\right.\" \/><\/figure>\n<p>On peut aussi l&rsquo;\u00e9crire sous une autre forme :<\/p>\n<figure class=\"wp-block-image\"><img decoding=\"async\" src=\"https:\/\/latex.codecogs.com\/gif.latex?\\begin{pmatrix}&amp;space;x&amp;space;\\\\&amp;space;y&amp;space;\\\\&amp;space;z&amp;space;\\end{pmatrix}&amp;space;=&amp;space;\\begin{pmatrix}&amp;space;x_0&amp;space;\\\\&amp;space;y_0&amp;space;\\\\&amp;space;z_0&amp;space;\\end{pmatrix}&amp;space;+k&amp;space;\\begin{pmatrix}&amp;space;x_v&amp;space;\\\\&amp;space;y_v&amp;space;\\\\&amp;space;z_v&amp;space;\\end{pmatrix}\" alt=\"\\begin{pmatrix} x \\\\ y \\\\ z \\end{pmatrix} = \\begin{pmatrix} x_0 \\\\ y_0 \\\\ z_0 \\end{pmatrix} +k \\begin{pmatrix} x_v \\\\ y_v \\\\ z_v \\end{pmatrix}\" \/><\/figure>\n<p>Dans cette repr\u00e9sentation <em>x<sub>0<\/sub><\/em>, <em>y<sub>0<\/sub><\/em> et <em>z<sub>0<\/sub><\/em> sont les coordonn\u00e9es d&rsquo;un point appartenant \u00e0 la droite et <em>x<sub>v<\/sub><\/em>, <em>y<sub>v<\/sub><\/em> et <em>z<sub>v<\/sub> <\/em>sont les composantes d&rsquo;un vecteur parall\u00e8le \u00e0 la droite (<em>vecteur directeur<\/em>). Il existe une infinit\u00e9 de points sur une droite et une infinit\u00e9 de vecteurs parall\u00e8les \u00e0 une droite. Ainsi, selon le point et le vecteur choisis, il existe ainsi une infinit\u00e9 de repr\u00e9sentations vectorielles d&rsquo;une m\u00eame droite.<\/p>\n<p>Cliquez sur une image pour voir un exemple :<\/p>\n<p><a href=\"https:\/\/www.swisslearn.org\/?p=39065\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-39143\" src=\"https:\/\/www.swisslearn.org\/wp-content\/uploads\/2024\/06\/equation-droite-passant-par-2-points-01.png\" alt=\"\" width=\"287\" height=\"193\" \/><\/a> <a href=\"https:\/\/www.swisslearn.org\/?p=39107\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-39149\" src=\"https:\/\/www.swisslearn.org\/wp-content\/uploads\/2024\/06\/equation-droite-passant-par-2-points-02-good.png\" alt=\"\" width=\"268\" height=\"161\" \/><\/a> <a href=\"https:\/\/www.swisslearn.org\/?p=39122\"><img loading=\"lazy\" decoding=\"async\" class=\"alignnone wp-image-39150\" src=\"https:\/\/www.swisslearn.org\/wp-content\/uploads\/2024\/06\/equation-droite-passant-par-2-points-03-1.png\" alt=\"\" width=\"243\" height=\"191\" \/><\/a><\/p>\n<p>Pour savoir comment d\u00e9terminer la partie visible d&rsquo;une droite, <a href=\"https:\/\/www.swisslearn.org\/?p=38803\" data-type=\"post\" data-id=\"38803\">cliquez ici<\/a>.<\/p>\n<p><!-- \/wp:embed --><\/p>\n","protected":false},"excerpt":{"rendered":"<p>La repr\u00e9sentation vectorielle ou param\u00e9trique d&rsquo;une droite dans l&rsquo;espace est de type : On peut aussi l&rsquo;\u00e9crire sous une autre forme : Dans cette repr\u00e9sentation x0, y0 et z0 sont les coordonn\u00e9es d&rsquo;un point appartenant \u00e0 la droite et xv, yv et zv sont les composantes d&rsquo;un vecteur parall\u00e8le \u00e0 la droite (vecteur directeur). Il [&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":[38,10,58],"tags":[],"class_list":["post-39141","post","type-post","status-publish","format-standard","hentry","category-cours","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=38\" rel=\"category\">Cours<\/a> <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":"La repr\u00e9sentation vectorielle ou param\u00e9trique d&rsquo;une droite dans l&rsquo;espace est de type : On peut aussi l&rsquo;\u00e9crire sous une autre forme : Dans cette repr\u00e9sentation x0, y0 et z0 sont les coordonn\u00e9es d&rsquo;un point appartenant \u00e0 la droite et xv, yv et zv sont les composantes d&rsquo;un vecteur parall\u00e8le \u00e0 la droite (vecteur directeur). Il\u2026","_links":{"self":[{"href":"https:\/\/www.swisslearn.org\/index.php?rest_route=\/wp\/v2\/posts\/39141"}],"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=39141"}],"version-history":[{"count":4,"href":"https:\/\/www.swisslearn.org\/index.php?rest_route=\/wp\/v2\/posts\/39141\/revisions"}],"predecessor-version":[{"id":39193,"href":"https:\/\/www.swisslearn.org\/index.php?rest_route=\/wp\/v2\/posts\/39141\/revisions\/39193"}],"wp:attachment":[{"href":"https:\/\/www.swisslearn.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=39141"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.swisslearn.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=39141"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.swisslearn.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=39141"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}