{"id":3195,"date":"2024-04-22T16:36:18","date_gmt":"2024-04-22T14:36:18","guid":{"rendered":"https:\/\/mxth.dk\/?p=3195"},"modified":"2026-04-09T22:41:01","modified_gmt":"2026-04-09T20:41:01","slug":"planets-parameterfremstilling","status":"publish","type":"post","link":"https:\/\/mxth.dk\/?p=3195","title":{"rendered":"Planets parameterfremstilling"},"content":{"rendered":"\n<p class=\" eplus-wrapper\">Vi ser her p\u00e5 parameterfremstillingen for et plan. Den minder meget om det vi har snakket om for linjens parameterfremstilling men med et ekstra led p\u00e5.<\/p>\n\n\n\n<p class=\" has-text-align-center eplus-wrapper\">\\(\\begin{pmatrix}x\\\\y\\\\z\\end{pmatrix}=\\begin{pmatrix}x_0\\\\y_0\\\\z_0\\end{pmatrix}+t\\cdot\\begin{pmatrix}r_{1x}\\\\r_{1y}\\\\r_{1z}\\end{pmatrix}+s\\cdot\\begin{pmatrix}r_{2x}\\\\r_{2y}\\\\r_{2z}\\end{pmatrix}\\)<\/p>\n\n\n\n<p class=\" eplus-wrapper\">Vi skal derfor kende \u00e9t punkt men to retningsvektor. De to retningvektorer kan enten v\u00e6re opgivet, eller man kan beregne dem. Hvis vi skal regne os frem til dem skal vi som minimum kende tre punkter som ligger i planen.<\/p>\n\n\n\n<p class=\" eplus-wrapper\">Link til bogen: <a href=\"https:\/\/mathtxa.systime.dk\/?id=128\">https:\/\/mathtxa.systime.dk\/?id=128<\/a><\/p>\n\n\n\n<p class=\" eplus-wrapper\">Nedenst\u00e5ende er der opgaver som d\u00e6kker parameterfremstillingen for et plan.<\/p>\n\n\n<h2 class=\" wp-block-heading has-system-font-font-family eplus-wrapper eplus-styles-uid-856266\" style=\"font-style:normal;font-weight:200\">Opgaver til parameterfremstilling for et plan<\/h2>\n\n\n<p class=\" eplus-wrapper\">Link til Stenners side: <a href=\"https:\/\/sites.google.com\/view\/stenners-matematik\/vektorer-i-rummet#h.p_dRAr5vBd8Kz-\">https:\/\/sites.google.com\/view\/stenners-matematik\/vektorer-i-rummet#h.p_dRAr5vBd8Kz-<\/a><\/p>\n\n\n\n<style>\n  table, th, td {\n    border: 1px solid black;\n    border-collapse: collapse;\n  }\n<\/style>\n<table width=\"100%\" border=\"1\">\n  <thead>\n    <tr>\n      <th scope=\"col\" width=\"33%\" bgcolor=\"#3CB371\">Gr\u00f8n<\/th>\n      <th scope=\"col\" width=\"33%\" bgcolor=\"#FFA500\">Gul<\/th>\n      <th scope=\"col\" width=\"33%\" bgcolor=\"#DC143C\">R\u00f8d<\/th>\n    <\/tr>\n  <\/thead>\n  <tbody>\n    <tr>\n      <td>\n        <p><a href=\"\" target=\"_blank\" rel=\"noopener noreferrer\"><\/a><\/p>\n      <\/td>\n      <td>\n        <p><a href=\"https:\/\/mathtxa.systime.dk\/?id=376#c480\" target=\"_blank\" rel=\"noopener noreferrer\">matAhtx 1.12<\/a><\/p>\n      <\/td>\n      <td>\n        <p><a href=\"https:\/\/mxth.dk\/?page_id=3178#VRPP001\" target=\"_blank\" rel=\"noopener noreferrer\">VRPP001<\/a><\/p>\n      <\/td>\n    <\/tr>\n  <\/tbody>\n<\/table>\n\n\n\n<div class=\"wp-block-kadence-accordion alignnone\"><div class=\"kt-accordion-wrap kt-accordion-id3195_f2eecc-ae kt-accordion-has-2-panes kt-active-pane-0 kt-accordion-block kt-pane-header-alignment-left kt-accodion-icon-style-basic kt-accodion-icon-side-right\" style=\"max-width:none\"><div class=\"kt-accordion-inner-wrap\" data-allow-multiple-open=\"false\" data-start-open=\"none\">\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-1 kt-pane3195_74282c-cd\"><div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\">Facit<\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div><div class=\"kt-accordion-panel kt-accordion-panel-hidden\"><div class=\"kt-accordion-panel-inner\">\n<div class=\"wp-block-kadence-accordion alignnone\"><div class=\"kt-accordion-wrap kt-accordion-id3195_f20995-c1 kt-accordion-has-2-panes kt-active-pane-0 kt-accordion-block kt-pane-header-alignment-left kt-accodion-icon-style-basic kt-accodion-icon-side-right\" style=\"max-width:none\"><div class=\"kt-accordion-inner-wrap\" data-allow-multiple-open=\"false\" data-start-open=\"none\">\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-1 kt-pane3195_263dea-71\"><div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\">matAhtx 1.12<\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div><div class=\"kt-accordion-panel kt-accordion-panel-hidden\"><div class=\"kt-accordion-panel-inner\">\n<div class=\"wp-block-kadence-accordion alignnone\"><div class=\"kt-accordion-wrap kt-accordion-id3195_1c8b7f-47 kt-accordion-has-2-panes kt-active-pane-0 kt-accordion-block kt-pane-header-alignment-left kt-accodion-icon-style-basic kt-accodion-icon-side-right\" style=\"max-width:none\"><div class=\"kt-accordion-inner-wrap\" data-allow-multiple-open=\"false\" data-start-open=\"none\">\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-1 kt-pane3195_3e54fb-ef\"><div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\">a.<\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div><div class=\"kt-accordion-panel kt-accordion-panel-hidden\"><div class=\"kt-accordion-panel-inner\">\n<p class=\" eplus-wrapper\">Spidsen af pyramiden ligger lodret over centrum af grundfladen og har koordinaterne (2,5; 2,5; 9).<\/p>\n<\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-2 kt-pane3195_a1349f-da\"><div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\">b.<\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div><div class=\"kt-accordion-panel kt-accordion-panel-hidden\"><div class=\"kt-accordion-panel-inner\">\n<p class=\" eplus-wrapper\">\\(\\begin{pmatrix}x\\\\y\\\\z\\end{pmatrix}= \\begin{pmatrix}2,5-2,5s+2,5t\\\\2,5-2,5s-2,5t\\\\9-9s-9t\\end{pmatrix}\\)<\/p>\n\n\n\n<p class=\" eplus-wrapper\">&nbsp;\\(\\begin{pmatrix}x\\\\y\\\\z\\end{pmatrix}= \\begin{pmatrix} 2,5+2,5s+2,5t\\\\2,5-2,5s+2,5t\\\\9-9s-9t\\end{pmatrix}\\)<\/p>\n\n\n\n<p class=\" eplus-wrapper\">&nbsp;\\(\\begin{pmatrix}x\\\\y\\\\z\\end{pmatrix}= \\begin{pmatrix} 2,5+2,5s-2,5t\\\\2,5+2,5s+2,5t\\\\9-9s-9t\\end{pmatrix}\\)<\/p>\n\n\n\n<p class=\" eplus-wrapper\">&nbsp;\\(\\begin{pmatrix}x\\\\y\\\\z\\end{pmatrix}= \\begin{pmatrix} 2,5-2,5s-2,5t\\\\2,5+2,5s-2,5t\\\\9-9s-9t\\end{pmatrix}\\)<\/p>\n<\/div><\/div><\/div>\n<\/div><\/div><\/div>\n<\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-2 kt-pane3195_c280c3-21\"><div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\">VRPP001<\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div><div class=\"kt-accordion-panel kt-accordion-panel-hidden\"><div class=\"kt-accordion-panel-inner\">\n<p class=\" eplus-wrapper\">Da de to linjer sk\u00e6rer hinanden i punktet (1, 2, -3) ligger de to linjer i samme plan og derfor udsp\u00e6nder de to retningsvektorer planet og parameterfremstillingen for planet kan fx v\u00e6re<\/p>\n\n\n\n<p class=\" eplus-wrapper\">\\(\\begin{pmatrix}x\\\\y\\\\z\\end{pmatrix}= \\begin{pmatrix}1+s+2t\\\\2+s+t\\\\-3+2s+t\\end{pmatrix}\\)&nbsp;<\/p>\n<\/div><\/div><\/div>\n<\/div><\/div><\/div>\n<\/div><\/div><\/div>\n<\/div><\/div><\/div>\n\n\n<h2 class=\" wp-block-heading has-system-font-font-family eplus-wrapper eplus-styles-uid-856266\" style=\"font-style:normal;font-weight:200\">Opgaver til planets parameterfremstilling ud fra tre punkter<\/h2>\n\n\n<p class=\" eplus-wrapper\">Link til Stenners side: <a href=\"https:\/\/sites.google.com\/view\/stenners-matematik\/vektorer-i-rummet#h.p__yBOHA0i_EBN\">https:\/\/sites.google.com\/view\/stenners-matematik\/vektorer-i-rummet#h.p__yBOHA0i_EBN<\/a><\/p>\n\n\n\n<style>\n  table, th, td {\n    border: 1px solid black;\n    border-collapse: collapse;\n  }\n<\/style>\n<table width=\"100%\" border=\"1\">\n  <thead>\n    <tr>\n      <th scope=\"col\" width=\"33%\" bgcolor=\"#3CB371\">Gr\u00f8n<\/th>\n      <th scope=\"col\" width=\"33%\" bgcolor=\"#FFA500\">Gul<\/th>\n      <th scope=\"col\" width=\"33%\" bgcolor=\"#DC143C\">R\u00f8d<\/th>\n    <\/tr>\n  <\/thead>\n  <tbody>\n    <tr>\n      <td>\n        <p><a href=\"https:\/\/mathtxa.systime.dk\/?id=376#c479\" target=\"_blank\" rel=\"noopener noreferrer\">matAhtx 1.11<\/a><\/p>\n      <\/td>\n      <td>\n        <p><a href=\"https:\/\/mathtxa.systime.dk\/?id=376#c485\" target=\"_blank\" rel=\"noopener noreferrer\">matAhtx 1.13<\/a><\/p>\n      <\/td>\n      <td>\n        <p><a href=\"https:\/\/mathtxa.systime.dk\/?id=376#c489\" target=\"_blank\" rel=\"noopener noreferrer\">matAhtx 1.14<\/a><\/p>\n      <\/td>\n    <\/tr>\n    <tr>\n      <td>\n        <p><a href=\"https:\/\/mxth.dk\/?page_id=3178#VRPPUTP001\" target=\"_blank\" rel=\"noopener noreferrer\">VRPPUTP001<\/a><\/p>\n      <\/td>\n      <td>\n        <p><a href=\"\" target=\"_blank\" rel=\"noopener noreferrer\"><\/a><\/p>\n      <\/td>\n      <td>\n        <p><a href=\"https:\/\/mxth.dk\/?page_id=3178#VRPPUTP003\" target=\"_blank\" rel=\"noopener noreferrer\">VRPPUTP003<\/a><\/p>\n      <\/td>\n    <\/tr>\n    <tr>\n      <td>\n        <p><a href=\"https:\/\/mxth.dk\/?page_id=3178#VRPPUTP002\" target=\"_blank\" rel=\"noopener noreferrer\">VRPPUTP002<\/a><\/p>\n      <\/td>\n      <td>\n        <p><a href=\"\" target=\"_blank\" rel=\"noopener noreferrer\"><\/a><\/p>\n      <\/td>\n      <td>\n        <p><a href=\"\" target=\"_blank\" rel=\"noopener noreferrer\"><\/a><\/p>\n      <\/td>\n    <\/tr>\n  <\/tbody>\n<\/table>\n\n\n\n<div class=\"wp-block-kadence-accordion alignnone\"><div class=\"kt-accordion-wrap kt-accordion-id3195_f59559-3a kt-accordion-has-2-panes kt-active-pane-0 kt-accordion-block kt-pane-header-alignment-left kt-accodion-icon-style-basic kt-accodion-icon-side-right\" style=\"max-width:none\"><div class=\"kt-accordion-inner-wrap\" data-allow-multiple-open=\"false\" data-start-open=\"none\">\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-1 kt-pane3195_c746e3-31\"><div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\">Facit<\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div><div class=\"kt-accordion-panel kt-accordion-panel-hidden\"><div class=\"kt-accordion-panel-inner\">\n<div class=\"wp-block-kadence-accordion alignnone\"><div class=\"kt-accordion-wrap kt-accordion-id3195_a55e55-5d kt-accordion-has-6-panes kt-active-pane-0 kt-accordion-block kt-pane-header-alignment-left kt-accodion-icon-style-basic kt-accodion-icon-side-right\" style=\"max-width:none\"><div class=\"kt-accordion-inner-wrap\" data-allow-multiple-open=\"false\" data-start-open=\"none\">\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-1 kt-pane3195_f0e7c0-97\"><div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\">matAhtx 1.11<\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div><div class=\"kt-accordion-panel kt-accordion-panel-hidden\"><div class=\"kt-accordion-panel-inner\">\n<div class=\"wp-block-kadence-accordion alignnone\"><div class=\"kt-accordion-wrap kt-accordion-id3195_2c9ba7-3b kt-accordion-has-2-panes kt-active-pane-0 kt-accordion-block kt-pane-header-alignment-left kt-accodion-icon-style-basic kt-accodion-icon-side-right\" style=\"max-width:none\"><div class=\"kt-accordion-inner-wrap\" data-allow-multiple-open=\"false\" data-start-open=\"none\">\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-1 kt-pane3195_7eeace-3d\"><div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\">a.<\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div><div class=\"kt-accordion-panel kt-accordion-panel-hidden\"><div class=\"kt-accordion-panel-inner\">\n<p class=\" eplus-wrapper\">\\(\\begin{pmatrix}x\\\\y\\\\z\\end{pmatrix}= \\begin{pmatrix}-s-7t+1\\\\s+3t+4\\\\11s+10t-8\\end{pmatrix}\\)<\/p>\n<\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-2 kt-pane3195_0bca44-68\"><div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\">b.<\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div><div class=\"kt-accordion-panel kt-accordion-panel-hidden\"><div class=\"kt-accordion-panel-inner\">\n<p class=\" eplus-wrapper\">For parameterv\u00e6rdierne \\(s=-2\\) og \\(t=-4\\) findes koordinaterne til Q som ligger i planen \\(\\alpha\\).<\/p>\n<\/div><\/div><\/div>\n<\/div><\/div><\/div>\n<\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-2 kt-pane3195_109d4b-98\"><div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\">matAhtx 1.13<\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div><div class=\"kt-accordion-panel kt-accordion-panel-hidden\"><div class=\"kt-accordion-panel-inner\">\n<div class=\"wp-block-kadence-accordion alignnone\"><div class=\"kt-accordion-wrap kt-accordion-id3195_b928c0-c3 kt-accordion-has-3-panes kt-active-pane-0 kt-accordion-block kt-pane-header-alignment-left kt-accodion-icon-style-basic kt-accodion-icon-side-right\" style=\"max-width:none\"><div class=\"kt-accordion-inner-wrap\" data-allow-multiple-open=\"false\" data-start-open=\"none\">\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-1 kt-pane3195_9684d9-06\"><div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\">a.<\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div><div class=\"kt-accordion-panel kt-accordion-panel-hidden\"><div class=\"kt-accordion-panel-inner\">\n<p class=\" eplus-wrapper\">\\(\\begin{pmatrix}x\\\\y\\\\z\\end{pmatrix}= \\begin{pmatrix}2s\\\\4t\\\\2+s+0,5t\\end{pmatrix}\\)<\/p>\n<\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-2 kt-pane3195_839650-fa\"><div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\">b.<\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div><div class=\"kt-accordion-panel kt-accordion-panel-hidden\"><div class=\"kt-accordion-panel-inner\">\n<p class=\" eplus-wrapper\">\\(\\begin{pmatrix}x\\\\y\\\\z\\end{pmatrix}= \\begin{pmatrix}2s+2t\\\\0\\\\2+s-0,2t\\end{pmatrix}\\)<\/p>\n<\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-3 kt-pane3195_2edef6-de\"><div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\">c.<\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div><div class=\"kt-accordion-panel kt-accordion-panel-hidden\"><div class=\"kt-accordion-panel-inner\">\n<p class=\" eplus-wrapper\">\\(\\begin{pmatrix}x\\\\y\\\\z\\end{pmatrix}= \\begin{pmatrix}2t\\\\0\\\\2+t\\end{pmatrix}\\)<\/p>\n<\/div><\/div><\/div>\n<\/div><\/div><\/div>\n<\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-3 kt-pane3195_13e15b-bd\"><div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\">matAhtx 1.14<\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div><div class=\"kt-accordion-panel kt-accordion-panel-hidden\"><div class=\"kt-accordion-panel-inner\">\n<div class=\"wp-block-kadence-accordion alignnone\"><div class=\"kt-accordion-wrap kt-accordion-id3195_1650f6-06 kt-accordion-has-4-panes kt-active-pane-0 kt-accordion-block kt-pane-header-alignment-left kt-accodion-icon-style-basic kt-accodion-icon-side-right\" style=\"max-width:none\"><div class=\"kt-accordion-inner-wrap\" data-allow-multiple-open=\"false\" data-start-open=\"none\">\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-1 kt-pane3195_4c76eb-93\"><div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\">a.<\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div><div class=\"kt-accordion-panel kt-accordion-panel-hidden\"><div class=\"kt-accordion-panel-inner\">\n<p class=\" eplus-wrapper\">\\(\\begin{pmatrix}x\\\\y\\\\z\\end{pmatrix}= \\begin{pmatrix}3t\\\\0\\\\7t\\end{pmatrix}\\)<\/p>\n\n\n\n<p class=\" eplus-wrapper\">&nbsp;\\(\\begin{pmatrix}x\\\\y\\\\z\\end{pmatrix}= \\begin{pmatrix}-3t\\\\t\\\\5t\\end{pmatrix}\\)<\/p>\n\n\n\n<p class=\" eplus-wrapper\">&nbsp;\\(\\begin{pmatrix}x\\\\y\\\\z\\end{pmatrix}= \\begin{pmatrix}2t\\\\5t\\\\3,6t\\end{pmatrix}\\)<\/p>\n<\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-2 kt-pane3195_a8a097-19\"><div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\">b.<\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div><div class=\"kt-accordion-panel kt-accordion-panel-hidden\"><div class=\"kt-accordion-panel-inner\">\n<p class=\" eplus-wrapper\">\\(\\begin{pmatrix}x\\\\y\\\\z\\end{pmatrix}= \\begin{pmatrix}3-6s-t\\\\s+5t\\\\7-2s-3,4t\\end{pmatrix}\\)<\/p>\n<\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-3 kt-pane3195_8edcdf-09\"><div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\">c.<\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div><div class=\"kt-accordion-panel kt-accordion-panel-hidden\"><div class=\"kt-accordion-panel-inner\">\n<p class=\" eplus-wrapper\">\\(|\\vec{OQ_1}|=\\sqrt{58}=7,6158\\)<\/p>\n\n\n\n<p class=\" eplus-wrapper\">\\(|\\vec{OQ_2}|=\\sqrt{35}=5,9161\\)<\/p>\n\n\n\n<p class=\" eplus-wrapper\">\\(|\\vec{OQ_3}|=\\sqrt{58}=6,4777\\)<\/p>\n<\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-4 kt-pane3195_f9c8c7-b3\"><div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\">d.<\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div><div class=\"kt-accordion-panel kt-accordion-panel-hidden\"><div class=\"kt-accordion-panel-inner\">\n<p class=\" eplus-wrapper\">Tyngdepunktets koordinater er (0,67; 2; 5,2)<\/p>\n<\/div><\/div><\/div>\n<\/div><\/div><\/div>\n<\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-4 kt-pane3195_aae51e-4f\"><div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\">VRPPUT001<\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div><div class=\"kt-accordion-panel kt-accordion-panel-hidden\"><div class=\"kt-accordion-panel-inner\">\n<p class=\" eplus-wrapper\">Der er mange forskellige muligheder for at opstille ligningen for det samme plan ud fra de tre punkter. Den ene mulighed er&nbsp;<\/p>\n\n\n\n<p class=\" eplus-wrapper\">&nbsp;\\(\\begin{pmatrix}x\\\\y\\\\z\\end{pmatrix}= \\begin{pmatrix}1+3s-2t\\\\2+3s-2t\\\\3+3s-t\\end{pmatrix}\\)<\/p>\n<\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-5 kt-pane3195_9d8f57-6a\"><div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\">VRPPUT002<\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div><div class=\"kt-accordion-panel kt-accordion-panel-hidden\"><div class=\"kt-accordion-panel-inner\">\n<p class=\" eplus-wrapper\">Der er mange forskellige muligheder for at opstille ligningen for det samme plan ud fra de tre punkter. Den ene mulighed er&nbsp;<\/p>\n\n\n\n<p class=\" eplus-wrapper\">&nbsp;\\(\\begin{pmatrix}x\\\\y\\\\z\\end{pmatrix}= \\begin{pmatrix}1+s-2t\\\\1-2s+t\\\\1+2s-2t\\end{pmatrix}\\)<\/p>\n<\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-6 kt-pane3195_020a2f-84\"><div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\">VRPPUT003<\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div><div class=\"kt-accordion-panel kt-accordion-panel-hidden\"><div class=\"kt-accordion-panel-inner\">\n<p class=\" eplus-wrapper\">\\(\\begin{pmatrix}x\\\\y\\\\z\\end{pmatrix}= \\begin{pmatrix}3+t+s\\\\-1-2t\\\\2t-3s\\end{pmatrix}\\)<\/p>\n<\/div><\/div><\/div>\n<\/div><\/div><\/div>\n<\/div><\/div><\/div>\n<\/div><\/div><\/div>\n\n\n<h2 class=\" wp-block-heading has-system-font-font-family eplus-wrapper eplus-styles-uid-856266\" style=\"font-style:normal;font-weight:200\">Opgaver til planets parameterfremstilling &#8211; en linjes sk\u00e6rring med planet<\/h2>\n\n\n<p class=\" eplus-wrapper\">Link til Stenners side: <a href=\"https:\/\/sites.google.com\/view\/stenners-matematik\/vektorer-i-rummet#h.p_mjEOcWlB_N-2\">https:\/\/sites.google.com\/view\/stenners-matematik\/vektorer-i-rummet#h.p_mjEOcWlB_N-2<\/a><\/p>\n\n\n\n<style>\n  table, th, td {\n    border: 1px solid black;\n    border-collapse: collapse;\n  }\n<\/style>\n<table width=\"100%\" border=\"1\">\n  <thead>\n    <tr>\n      <th scope=\"col\" width=\"33%\" bgcolor=\"#3CB371\">Gr\u00f8n<\/th>\n      <th scope=\"col\" width=\"33%\" bgcolor=\"#FFA500\">Gul<\/th>\n      <th scope=\"col\" width=\"33%\" bgcolor=\"#DC143C\">R\u00f8d<\/th>\n    <\/tr>\n  <\/thead>\n  <tbody>\n    <tr>\n      <td>\n        <p><a href=\"https:\/\/mathtxa.systime.dk\/?id=376#c494\" target=\"_blank\" rel=\"noopener noreferrer\">matAhtx 1.15<\/a><\/p>\n      <\/td>\n      <td>\n        <p><a href=\"https:\/\/sites.google.com\/view\/stenners-matematik\/vektorer-i-rummet\/opgaver?authuser=0#h.p_yB7inQOhQzp5\" target=\"_blank\" rel=\"noopener noreferrer\">SMLP1<\/a><\/p>\n      <\/td>\n      <td>\n        <p><a href=\"https:\/\/sites.google.com\/view\/stenners-matematik\/vektorer-i-rummet\/opgaver?authuser=0#h.p_fg8bPet7SXvK\" target=\"_blank\" rel=\"noopener noreferrer\">SMLP2<\/a><\/p>\n      <\/td>\n    <\/tr>\n  <\/tbody>\n<\/table>\n\n\n\n<div class=\"wp-block-kadence-accordion alignnone\"><div class=\"kt-accordion-wrap kt-accordion-id3195_e0bca4-49 kt-accordion-has-2-panes kt-active-pane-0 kt-accordion-block kt-pane-header-alignment-left kt-accodion-icon-style-basic kt-accodion-icon-side-right\" style=\"max-width:none\"><div class=\"kt-accordion-inner-wrap\" data-allow-multiple-open=\"false\" data-start-open=\"none\">\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-1 kt-pane3195_e3386e-d4\"><div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\">Facit<\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div><div class=\"kt-accordion-panel kt-accordion-panel-hidden\"><div class=\"kt-accordion-panel-inner\">\n<div class=\"wp-block-kadence-accordion alignnone\"><div class=\"kt-accordion-wrap kt-accordion-id3195_6e2d1f-5a kt-accordion-has-3-panes kt-active-pane-0 kt-accordion-block kt-pane-header-alignment-left kt-accodion-icon-style-basic kt-accodion-icon-side-right\" style=\"max-width:none\"><div class=\"kt-accordion-inner-wrap\" data-allow-multiple-open=\"false\" data-start-open=\"none\">\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-1 kt-pane3195_d5d653-6b\"><div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\">matAhtx 1.15<\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div><div class=\"kt-accordion-panel kt-accordion-panel-hidden\"><div class=\"kt-accordion-panel-inner\">\n<p class=\" eplus-wrapper\">Koordinater for sk\u00e6rringspunktet er \\(\\begin{pmatrix}\\frac{293}{18},\\frac{1357}{36},\\frac{325}{4}\\end{pmatrix}=(16,2777; 37,6944; 81,25)\\)<\/p>\n<\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-2 kt-pane3195_18963f-54\"><div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\">SMLP1<\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div><div class=\"kt-accordion-panel kt-accordion-panel-hidden\"><div class=\"kt-accordion-panel-inner\">\n<div class=\"wp-block-kadence-accordion alignnone\"><div class=\"kt-accordion-wrap kt-accordion-id3195_2eae32-b9 kt-accordion-has-3-panes kt-active-pane-0 kt-accordion-block kt-pane-header-alignment-left kt-accodion-icon-style-basic kt-accodion-icon-side-right\" style=\"max-width:none\"><div class=\"kt-accordion-inner-wrap\" data-allow-multiple-open=\"false\" data-start-open=\"none\">\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-1 kt-pane3195_f593de-22\"><div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\">1.<\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div><div class=\"kt-accordion-panel kt-accordion-panel-hidden\"><div class=\"kt-accordion-panel-inner\">\n<p class=\" eplus-wrapper\">Der er ingen sk\u00e6ringspunkter.<\/p>\n<\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-2 kt-pane3195_a92b84-09\"><div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\">2.<\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div><div class=\"kt-accordion-panel kt-accordion-panel-hidden\"><div class=\"kt-accordion-panel-inner\">\n<p class=\" eplus-wrapper\">Dette skyldes at planet og linjen er parallelle.<\/p>\n<\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-3 kt-pane3195_c916cd-5d\"><div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\">3.<\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div><div class=\"kt-accordion-panel kt-accordion-panel-hidden\"><div class=\"kt-accordion-panel-inner\">\n<p class=\" eplus-wrapper\"><a href=\"https:\/\/www.geogebra.org\/calculator\/tfstkmhu\" target=\"_blank\" rel=\"noreferrer noopener nofollow\">https:\/\/www.geogebra.org\/calculator\/tfstkmhu<\/a><\/p>\n<\/div><\/div><\/div>\n<\/div><\/div><\/div>\n<\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-3 kt-pane3195_25d644-7b\"><div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\">SMLP2<\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div><div class=\"kt-accordion-panel kt-accordion-panel-hidden\"><div class=\"kt-accordion-panel-inner\">\n<div class=\"wp-block-kadence-accordion alignnone\"><div class=\"kt-accordion-wrap kt-accordion-id3195_42c3e3-c5 kt-accordion-has-3-panes kt-active-pane-0 kt-accordion-block kt-pane-header-alignment-left kt-accodion-icon-style-basic kt-accodion-icon-side-right\" style=\"max-width:none\"><div class=\"kt-accordion-inner-wrap\" data-allow-multiple-open=\"false\" data-start-open=\"none\">\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-1 kt-pane3195_9c8f3b-3c\"><div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\">1.<\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div><div class=\"kt-accordion-panel kt-accordion-panel-hidden\"><div class=\"kt-accordion-panel-inner\">\n<p class=\" eplus-wrapper\">Der er ingen sk\u00e6ringspunkter<\/p>\n<\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-2 kt-pane3195_3d3b47-58\"><div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\">2.<\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div><div class=\"kt-accordion-panel kt-accordion-panel-hidden\"><div class=\"kt-accordion-panel-inner\">\n<p class=\" eplus-wrapper\">Dette skyldes at planet og linjen er parallelle<\/p>\n<\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-3 kt-pane3195_eda6a0-d9\"><div class=\"kt-accordion-header-wrap\"><button class=\"kt-blocks-accordion-header kt-acccordion-button-label-show\"><span class=\"kt-blocks-accordion-title-wrap\"><span class=\"kt-blocks-accordion-title\">3.<\/span><\/span><span class=\"kt-blocks-accordion-icon-trigger\"><\/span><\/button><\/div><div class=\"kt-accordion-panel kt-accordion-panel-hidden\"><div class=\"kt-accordion-panel-inner\">\n<p class=\" eplus-wrapper\"><a href=\"https:\/\/www.geogebra.org\/calculator\/b2tb5gtr\" target=\"_blank\" rel=\"noreferrer noopener nofollow\">https:\/\/www.geogebra.org\/calculator\/b2tb5gtr<\/a><\/p>\n<\/div><\/div><\/div>\n<\/div><\/div><\/div>\n<\/div><\/div><\/div>\n<\/div><\/div><\/div>\n<\/div><\/div><\/div>\n<\/div><\/div><\/div>\n","protected":false},"excerpt":{"rendered":"<p>Vi ser her p\u00e5 parameterfremstillingen for et plan. Den minder meget om det vi har snakket om for linjens parameterfremstilling men med et ekstra led p\u00e5. Vi skal derfor kende \u00e9t punkt, men to retningsvektor. De to retningvektorer kan enten v\u00e6re opgivet, eller man kan beregne dem. Hvis vi skal regne os frem til dem skal vi som minimum kende tre punkter som ligger i planen. <\/p>\n<p>Nedenst\u00e5ende er der opgaver som d\u00e6kker parameterfremstillingen for et plan.<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"closed","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"ub_ctt_via":"","editor_plus_copied_stylings":"{}","_jetpack_memberships_contains_paid_content":false,"footnotes":""},"categories":[3,60],"tags":[74],"class_list":["post-3195","post","type-post","status-publish","format-standard","hentry","category-matematik","category-vektorer-i-rummet","tag-htx"],"featured_image_src":null,"author_info":{"display_name":"Henriksen","author_link":"https:\/\/mxth.dk\/?author=1"},"jetpack_featured_media_url":"","jetpack_sharing_enabled":true,"_links":{"self":[{"href":"https:\/\/mxth.dk\/index.php?rest_route=\/wp\/v2\/posts\/3195","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/mxth.dk\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/mxth.dk\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/mxth.dk\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/mxth.dk\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=3195"}],"version-history":[{"count":9,"href":"https:\/\/mxth.dk\/index.php?rest_route=\/wp\/v2\/posts\/3195\/revisions"}],"predecessor-version":[{"id":3280,"href":"https:\/\/mxth.dk\/index.php?rest_route=\/wp\/v2\/posts\/3195\/revisions\/3280"}],"wp:attachment":[{"href":"https:\/\/mxth.dk\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3195"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mxth.dk\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3195"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mxth.dk\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3195"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}