{"id":3228,"date":"2024-05-03T00:17:51","date_gmt":"2024-05-02T22:17:51","guid":{"rendered":"https:\/\/mxth.dk\/?p=3228"},"modified":"2026-04-09T22:41:01","modified_gmt":"2026-04-09T20:41:01","slug":"skaeringer-og-vinkler-i-rummet","status":"publish","type":"post","link":"https:\/\/mxth.dk\/?p=3228","title":{"rendered":"Sk\u00e6ringer og vinkler i rummet"},"content":{"rendered":"\n<p class=\" eplus-wrapper\">Vi ser her p\u00e5 sk\u00e6ringer og vinkler i rummet. Vi starter med at se p\u00e5 to planer i rummet og hvordan vi finder sk\u00e6ringen mellem disse og derefter hvorledes vi kan finde vinklen mellem disse.<\/p>\n\n\n\n<p class=\" eplus-wrapper\">Herefter ser vi p\u00e5 sk\u00e6ringen mellem en linje og et plan og til sidst vinklen mellem en linje i rummet og 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\">Sk\u00e6ringslinje mellem to planer<\/h2>\n\n\n<p class=\" eplus-wrapper\">Link til bogen: <a href=\"https:\/\/mathtxa.systime.dk\/?id=131\">https:\/\/mathtxa.systime.dk\/?id=131<\/a><\/p>\n\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_rLBUKRDJon9I\">https:\/\/sites.google.com\/view\/stenners-matematik\/vektorer-i-rummet#h.p_rLBUKRDJon9I<\/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:\/\/sites.google.com\/view\/matematikopgaver\/start\/systime-matbastx-2010\/mere-rumgeometri#h.chcepqxrtzob\" target=\"_blank\" rel=\"noopener noreferrer\">matBAstx 1201<\/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:\/\/sites.google.com\/view\/matematikopgaver\/start\/systime-matbastx-2010\/mere-rumgeometri#h.a30onsluud35\" target=\"_blank\" rel=\"noopener noreferrer\">matBAstx 1203<\/a><\/p>\n      <\/td>\n    <\/tr>\n    <tr>\n      <td>\n        <p><a href=\"https:\/\/sites.google.com\/view\/matematikopgaver\/start\/systime-matbastx-2010\/mere-rumgeometri#h.1q9p57ongh5i\" target=\"_blank\" rel=\"noopener noreferrer\">matBAstx 1202<\/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-id3228_d0c559-35 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-pane3228_5b3e6a-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\">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-id3228_a5827b-d2 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-pane3228_bfe76b-2e\"><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\">matBAstx 1201<\/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\">Parameterfremstillingen for linjen er \\(\\begin{pmatrix}x\\\\y\\\\z\\end{pmatrix}=\\begin{pmatrix}0-11\\cdot t\\\\\\frac{29}{11}+19\\cdot t\\\\\\frac{34}{11}+31\\cdot t\\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-pane3228_ad28fe-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\">matBAstx 1202<\/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\">Parameterfremstillingen for linjen er \\(\\begin{pmatrix}x\\\\y\\\\z\\end{pmatrix}=\\begin{pmatrix}0\\\\\\frac{35}{106}+30\\cdot t\\\\-\\frac{95}{106}+50\\cdot t\\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-pane3228_d833e6-03\"><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\">matBAstx 1203<\/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\">V\u00e6rdien af k er -6 og koordinaterne til sk\u00e6ringspunktet er (0,0,-6) og linjen \\(m\\) har parameterfremstillingen \\(\\begin{pmatrix}x\\\\y\\\\z\\end{pmatrix}=\\begin{pmatrix}-t\\\\5\\cdot t\\\\-6+28\\cdot t\\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\">Sk\u00e6ringsvinkel mellem to planer<\/h2>\n\n\n<p class=\" eplus-wrapper\">Link til bogen: <a href=\"https:\/\/mathtxa.systime.dk\/?id=132\">https:\/\/mathtxa.systime.dk\/?id=132<\/a><\/p>\n\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_S_GeHJzB4nPr\">https:\/\/sites.google.com\/view\/stenners-matematik\/vektorer-i-rummet#h.p_S_GeHJzB4nPr<\/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:\/\/sites.google.com\/view\/matematikopgaverpmtekmatr4\/15-vektorer-i-rummet\/sk\u00e6ringer-og-vinkler\/opgave-498\" target=\"_blank\" rel=\"noopener noreferrer\">PM4-498<\/a><\/p>\n      <\/td>\n      <td>\n        <p><a href=\"https:\/\/sites.google.com\/view\/matematikopgaverpmtekmatr4\/15-vektorer-i-rummet\/sk\u00e6ringer-og-vinkler\/opgave-501\" target=\"_blank\" rel=\"noopener noreferrer\">PM4-501<\/a><\/p>\n      <\/td>\n      <td>\n        <p><a href=\"\" target=\"_blank\" rel=\"noopener noreferrer\"><\/a><\/p>\n      <\/td>\n    <\/tr>\n    <tr>\n      <td>\n        <p><a href=\"https:\/\/sites.google.com\/view\/matematikopgaver\/start\/systime-mata3stx-2010\/rumgeometri#h.f3yn3yitqt6v\" target=\"_blank\" rel=\"noopener noreferrer\">matA3stx 545<\/a><\/p>\n      <\/td>\n      <td>\n        <p><a href=\"https:\/\/sites.google.com\/view\/matematikopgaver\/start\/systime-mata3stx-2010\/rumgeometri#h.ktys9sfcla43\" target=\"_blank\" rel=\"noopener noreferrer\">matA3stx 547<\/a><\/p>\n      <\/td>\n      <td>\n        <p><a href=\"\" target=\"_blank\" rel=\"noopener noreferrer\"><\/a><\/p>\n      <\/td>\n    <\/tr>\n    <tr>\n      <td>\n        <p><a href=\"https:\/\/sites.google.com\/view\/matematikopgaver\/start\/systime-mata3stx-2010\/rumgeometri#h.88hk60al4ynq\" target=\"_blank\" rel=\"noopener noreferrer\">matA3stx 546<\/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    <tr>\n      <td>\n        <p><a href=\"https:\/\/sites.google.com\/view\/matematikopgaver\/start\/systime-htx-mat-a\/vektorer-i-rummet#h.htqd0ldl97y5\" target=\"_blank\" rel=\"noopener noreferrer\">matAhtx 1.23<\/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    <tr>\n      <td>\n        <p><a href=\"https:\/\/sites.google.com\/view\/matematikopgaver\/start\/systime-htx-mat-a\/vektorer-i-rummet#h.htqd0ldl97y5\" target=\"_blank\" rel=\"noopener noreferrer\">PM4-497<\/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    <tr>\n      <td>\n        <p><a href=\"https:\/\/sites.google.com\/view\/matematikopgaver\/start\/systime-mata3stx-2010\/rumgeometri#h.xd5hzdqjakl6\" target=\"_blank\" rel=\"noopener noreferrer\">matA3stx 548<\/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-id3228_2e2ac6-b9 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-pane3228_e8c0b3-76\"><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-id3228_d5e9cd-4d kt-accordion-has-8-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-pane3228_9cbc4e-59\"><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\">PM4-498<\/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\">Vinklen mellem de to planer er \\(68^\\circ\\).<\/p>\n<\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-2 kt-pane3228_c733e8-72\"><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\">matA3stx 545<\/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\">Vinklen mellem de to planer er \\(70,8^\\circ\\).<\/p>\n<\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-3 kt-pane3228_7ea960-0c\"><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\">matA3stx 546<\/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\">Vinklen mellem de to planer er \\(77,2^\\circ\\)&nbsp;.<\/p>\n<\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-4 kt-pane3228_bac171-d2\"><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 1.23<\/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-id3228_b8ff44-e8 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-pane3228_09b731-5b\"><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\">Parameterfremstillingen for sk\u00e6ringslinjen er \\(\\begin{pmatrix}x\\\\y\\\\z\\end{pmatrix}=\\begin{pmatrix}-30\\cdot t\\\\-3,3 &#8211; 15 cdot t\\\\0,4\\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-pane3228_cd7314-4e\"><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\">Vinklen mellem de to planer er \\(76,6^\\circ\\)<\/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-5 kt-pane3228_670b94-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\">PM4-497<\/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-id3228_511570-ac 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-pane3228_7a2951-6e\"><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\">Parameterfremstillingen for sk\u00e6ringslinjen er \\(\\begin{pmatrix}x\\\\y\\\\z\\end{pmatrix}=\\begin{pmatrix}t\\\\32 + 14 cdot t\\\\84+37\\cdot t\\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-pane3228_1a3646-67\"><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\">Vinklen mellem de to planer er \\(51^\\circ\\).<\/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-6 kt-pane3228_3f01dd-ba\"><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\">matA3stx 548<\/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\">Vinklen mellem de to planer er \\(19,5^\\circ\\)<\/p>\n<\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-7 kt-pane3228_2f9665-d8\"><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\">PM4-501<\/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-id3228_0cf4f8-09 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-pane3228_55079a-4a\"><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\">Vinklen mellem to skr\u00e5 sideflader, der ligger over for hinanden er \\(33,4^\\circ\\).<\/p>\n<\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-2 kt-pane3228_6b24e7-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\">Vinklen melllem to skr\u00e5 sideflader, der st\u00f8der op til hinanden er \\(94,7^\\circ\\)<\/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-8 kt-pane3228_f7bb4d-a9\"><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\">matA3stx 547<\/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\">Vinklen mellem de to planer er \\(63,1^\\circ\\)<\/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\">Sk\u00e6ringspunkt mellem linje og plan<\/h2>\n\n\n<p class=\" eplus-wrapper\">Link til bogen: <a href=\"https:\/\/mathtxa.systime.dk\/?id=133\">https:\/\/mathtxa.systime.dk\/?id=133<\/a><\/p>\n\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_aFBy3lNA4oVc\">https:\/\/sites.google.com\/view\/stenners-matematik\/vektorer-i-rummet#h.p_aFBy3lNA4oVc<\/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:\/\/mxth.dk\/?page_id=3178#VRSMLP001\" target=\"_blank\" rel=\"noopener noreferrer\">VRSMLP001<\/a><\/p>\n      <\/td>\n      <td>\n        <p><a href=\"https:\/\/mxth.dk\/?page_id=3178#VRSMLP002\" target=\"_blank\" rel=\"noopener noreferrer\">VRSMLP002<\/a><\/p>\n      <\/td>\n      <td>\n        <p><a href=\"\" target=\"_blank\" rel=\"noopener noreferrer\"><\/a><\/p>\n      <\/td>\n    <\/tr>\n    <tr>\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#VRSMLP003\" target=\"_blank\" rel=\"noopener noreferrer\">VRSMLP003<\/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-id3228_8e16af-84 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-pane3228_4b05c2-b9\"><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-id3228_e5c6c3-d7 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-pane3228_c12627-68\"><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\">VRSMLP001<\/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\">Sk\u00e6ringspunktet mellem linjen og planet er (\\(\\frac{41}{4}, \\frac{9}{2},\\frac{5}{4}\\)) = (10,25; 4,5; 1,25)<\/p>\n<\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-2 kt-pane3228_3e28a8-b7\"><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\">VRSMLP002<\/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\">Sk\u00e6ringspunktet mellem linjen og planet er (\\(\\frac{29}{21}, -\\frac{10}{7},\\frac{71}{21}\\))<\/p>\n<\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-3 kt-pane3228_9e1514-bb\"><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\">VRSMLP003<\/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 skalarproduktet mellem retningsvektoren og normalvektoren ikke er nul, er de to vektorer ikke vinkelrette og derved er retningsvektoren ikke parallel med planet.&nbsp;<\/p>\n\n\n\n<p class=\" eplus-wrapper\">Sk\u00e6ringspunktet bliver derfor (5,0,5).<\/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\">Sk\u00e6ringsvinkel mellem en linje og et plan<\/h2>\n\n\n<p class=\" eplus-wrapper\">Link til bogen: <a href=\"https:\/\/mathtxa.systime.dk\/?id=134\">https:\/\/mathtxa.systime.dk\/?id=134<\/a><\/p>\n\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_YjPgDnb57cNS\">https:\/\/sites.google.com\/view\/stenners-matematik\/vektorer-i-rummet#h.p_YjPgDnb57cNS<\/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:\/\/sites.google.com\/view\/matematikopgaver\/start\/systime-mata3stx-2010\/rumgeometri#h.f1sew2gf2muk\" target=\"_blank\" rel=\"noopener noreferrer\">matA3stx 549<\/a><\/p>\n      <\/td>\n      <td>\n        <p><a href=\"https:\/\/sites.google.com\/view\/matematikopgaver\/start\/systime-mata3stx-2010\/rumgeometri#h.2rbhd9tadc0i\" target=\"_blank\" rel=\"noopener noreferrer\">matA3stx 552<\/a><\/p>\n      <\/td>\n      <td>\n        <p><a href=\"https:\/\/sites.google.com\/view\/matematikopgaver\/start\/systime-mata3stx-2010\/rumgeometri#h.jilxw7k2z40a\" target=\"_blank\" rel=\"noopener noreferrer\">matA3stx 550<\/a><\/p>\n      <\/td>\n    <\/tr>\n    <tr>\n      <td>\n        <p><a href=\"https:\/\/sites.google.com\/view\/matematikopgaver\/start\/systime-mata3stx-2010\/rumgeometri#h.hinztvhxobhn\" target=\"_blank\" rel=\"noopener noreferrer\">matA3stx 551<\/a><\/p>\n      <\/td>\n      <td>\n        <p><a href=\"https:\/\/sites.google.com\/view\/matematikopgaverpmtekmatr4\/15-vektorer-i-rummet\/sk\u00e6ringer-og-vinkler\/opgave-500\" target=\"_blank\" rel=\"noopener noreferrer\">PM4-500<\/a><\/p>\n      <\/td>\n      <td>\n        <p><a href=\"https:\/\/sites.google.com\/view\/matematikopgaver\/start\/systime-mata3stx-2010\/rumgeometri#h.p0c7cll8j4og\" target=\"_blank\" rel=\"noopener noreferrer\">matA3stx 553<\/a><\/p>\n      <\/td>\n    <\/tr>\n    <tr>\n      <td>\n        <p><a href=\"https:\/\/sites.google.com\/view\/matematikopgaverpmtekmatr4\/15-vektorer-i-rummet\/sk\u00e6ringer-og-vinkler\/opgave-499\" target=\"_blank\" rel=\"noopener noreferrer\">PM4-499<\/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:\/\/sites.google.com\/view\/matematikopgaver\/start\/systime-htx-mat-a\/vektorer-i-rummet#h.a81exxkyccvo\" target=\"_blank\" rel=\"noopener noreferrer\">matAhtx 1.24<\/a><\/p>\n      <\/td>\n    <\/tr>\n  <\/tbody>\n<\/table>\n","protected":false},"excerpt":{"rendered":"<p>Vi ser her p\u00e5 sk\u00e6ringer og vinkler i rummet. Vi starter med at se p\u00e5 to planer i rummet og hvordan vi finder sk\u00e6ringen mellem disse og derefter hvorledes vi kan finde vinklen mellem disse. Herefter ser vi p\u00e5 sk\u00e6ringen mellem en linje og et plan og til sidst vinklen mellem en linje i rummet [&hellip;]<\/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-3228","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\/3228","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=3228"}],"version-history":[{"count":15,"href":"https:\/\/mxth.dk\/index.php?rest_route=\/wp\/v2\/posts\/3228\/revisions"}],"predecessor-version":[{"id":3297,"href":"https:\/\/mxth.dk\/index.php?rest_route=\/wp\/v2\/posts\/3228\/revisions\/3297"}],"wp:attachment":[{"href":"https:\/\/mxth.dk\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3228"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mxth.dk\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3228"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mxth.dk\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3228"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}