{"id":3967,"date":"2022-08-05T17:37:33","date_gmt":"2022-08-05T15:37:33","guid":{"rendered":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/kolmost-primek-a-rovin-priklad\/"},"modified":"2022-08-05T17:47:17","modified_gmt":"2022-08-05T15:47:17","slug":"kolmost-primek-a-rovin-reseny-priklad","status":"publish","type":"lesson","link":"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/kolmost-primek-a-rovin-reseny-priklad\/","title":{"rendered":"Kolmost p\u0159\u00edmek a rovin \u0159e\u0161en\u00fd p\u0159\u00edklad"},"content":{"rendered":"<p><strong>Zad\u00e1n\u00ed:<\/strong><\/p>\n<p>Napi\u0161te obecnou rovnici roviny, kter\u00e1 proch\u00e1z\u00ed bodem <em><strong>A [7;-5;3]<\/strong> <\/em>a je kolm\u00e1 k p\u0159\u00edmce s parametrick\u00fdm vyj\u00e1d\u0159en\u00edm\u00a0<\/p>\n<p><em><strong>x=2+3t<\/strong><\/em><\/p>\n<p><em><strong>y=5t<\/strong><\/em><\/p>\n<p><em><strong>z=7-2t, t\u20act<\/strong><\/em><\/p>\n<p><strong>\u0158e\u0161en\u00ed:<\/strong><\/p>\n<p>Rovinu si m\u016f\u017eeme ozna\u010dit p\u00edsmenem <em><strong>\u03b1<\/strong><\/em> a za\u010dneme t\u00edm, \u017ee sestav\u00edme jej\u00ed parametrickou rovnici, kter\u00e1 vypad\u00e1 n\u00e1sledovn\u011b:<\/p>\n<p>$$\u03b1=ax+by+cz+d$$<\/p>\n<p>$$\u03b1=3x+5x-2z+d=0$$<\/p>\n<p>n\u00e1sledn\u011b dosad\u00edme bod A do rovnice a z\u00edsk\u00e1me:<\/p>\n<p>$$A\u2208\u03b1=3\\cdot7+5\\cdot(-5)-2\\cdot3+d=0$$<\/p>\n<p>$$A\u2208\u03b1=21-25-6+d=0$$\u00a0<\/p>\n<p>$$d=10$$<\/p>\n<p>Dostaneme tedy obecnou rovnici roviny, kter\u00e1 proch\u00e1z\u00ed bodem A je kolm\u00e1 k zadan\u00e9 p\u0159\u00edmce.<\/p>\n<p style=\"text-align: center\">$$3x+5y-2z+10=0$$<\/p>\n","protected":false},"comment_status":"open","ping_status":"closed","template":"","class_list":["post-3967","lesson","type-lesson","status-publish","hentry"],"yoast_head":"<!-- This site is optimized with the Yoast SEO plugin v27.5 - https:\/\/yoast.com\/product\/yoast-seo-wordpress\/ -->\n<title>Kolmost p\u0159\u00edmek a rovin \u0159e\u0161en\u00fd p\u0159\u00edklad | Studijni-svet.cz<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/studijni-svet.cz\/kurzy\/courses\/matematika-k-maturite\/lekce\/kolmost-primek-a-rovin-reseny-priklad\/\" \/>\n<meta property=\"og:locale\" content=\"cs_CZ\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"Kolmost p\u0159\u00edmek a rovin \u0159e\u0161en\u00fd p\u0159\u00edklad | Studijni-svet.cz\" \/>\n<meta property=\"og:description\" content=\"Zad\u00e1n\u00ed: Napi\u0161te obecnou rovnici roviny, kter\u00e1 proch\u00e1z\u00ed bodem A [7;-5;3] a je kolm\u00e1 k p\u0159\u00edmce s parametrick\u00fdm vyj\u00e1d\u0159en\u00edm\u00a0 x=2+3t y=5t z=7-2t, t\u20act \u0158e\u0161en\u00ed: Rovinu si m\u016f\u017eeme ozna\u010dit p\u00edsmenem \u03b1 a za\u010dneme t\u00edm, \u017ee sestav\u00edme jej\u00ed parametrickou rovnici, kter\u00e1 vypad\u00e1 n\u00e1sledovn\u011b: $$\u03b1=ax+by+cz+d$$ $$\u03b1=3x+5x-2z+d=0$$ n\u00e1sledn\u011b dosad\u00edme bod A do rovnice a z\u00edsk\u00e1me: $$A\u2208\u03b1=3cdot7+5cdot(-5)-2cdot3+d=0$$ $$A\u2208\u03b1=21-25-6+d=0$$\u00a0 $$d=10$$ Dostaneme tedy ... 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