{"id":3208,"date":"2024-04-29T21:37:46","date_gmt":"2024-04-29T19:37:46","guid":{"rendered":"https:\/\/mxth.dk\/?p=3208"},"modified":"2026-04-09T22:41:01","modified_gmt":"2026-04-09T20:41:01","slug":"vektorprodukt","status":"publish","type":"post","link":"https:\/\/mxth.dk\/?p=3208","title":{"rendered":"Vektorprodukt"},"content":{"rendered":"\n<p class=\" eplus-wrapper\">Ogs\u00e5 kaldet krydsprudukt, er en m\u00e5de man kan \u201cgange\u201d vektorer sammen lige som skalarproduktet. Hvor skalarproduktet g\u00e6lder for b\u00e5de vektorer i planet og i rummet og giver et tal, der af navnet, g\u00e6lder vektorproduktet kun for vektorer i rummet og giver endnu en tredje vektor som st\u00e5r vinkelret p\u00e5 begge de to vektorer som blev krydset sammen.<\/p>\n\n\n\n<p class=\" eplus-wrapper\">Formlen for udregningen af vektorproduktet er <\/p>\n\n\n\n<p class=\" has-text-align-center eplus-wrapper\">\\(\\vec{a}\\times\\vec{b}=\\begin{pmatrix}a_2\\cdot b_3 &#8211; a_3\\cdot b_2\\\\a_3\\cdot b_1 &#8211; a_1\\cdot b_3\\\\a_1\\cdot b_2 &#8211; a_2\\cdot b_1\\end{pmatrix}\\)<\/p>\n\n\n\n<p class=\" eplus-wrapper\">Link til bogen: <a href=\"https:\/\/mathtxa.systime.dk\/?id=129\">https:\/\/mathtxa.systime.dk\/?id=129<\/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_0x92CNewZ7lg\">https:\/\/sites.google.com\/view\/stenners-matematik\/vektorer-i-rummet#h.p_0x92CNewZ7lg<\/a><\/p>\n\n\n\n<p class=\" eplus-wrapper\">Link til Stenners bevis for vektorprodukt: <a href=\"https:\/\/sites.google.com\/view\/stenners-matematik\/vektorer-i-rummet#h.289ebbe1xqj3\">https:\/\/sites.google.com\/view\/stenners-matematik\/vektorer-i-rummet#h.289ebbe1xqj3<\/a><\/p>\n\n\n<p class=\" has-system-font-font-family eplus-wrapper eplus-styles-uid-4f3c87\" style=\"font-style:normal;font-weight:200\">Opgaver<\/p>\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\/vektorprodukt\/opgave-488\" target=\"_blank\" rel=\"noopener noreferrer\">PM4-488<\/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\/matematikopgaverpmtekmatr4\/15-vektorer-i-rummet\/vektorprodukt\/opgave-489\" target=\"_blank\" rel=\"noopener noreferrer\">PM4-489<\/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\/matematikopgaverpmtekmatr4\/15-vektorer-i-rummet\/vektorprodukt\/opgave-490\" target=\"_blank\" rel=\"noopener noreferrer\">PM4-490<\/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-id3208_998667-b0 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-pane3208_1c99cb-3e\"><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-id3208_b1660c-9e 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-pane3208_7f7e55-55\"><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\">PM4-488<\/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-id3208_304096-56 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-pane3208_4b227b-75\"><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 de to vektorer er \\(96,5^\\circ\\).<\/p>\n<\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-2 kt-pane3208_fa5986-13\"><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\">Vektoren bestemt ved vektorproduktet mellem \\(vec{a}\\) og \\(\\vec{b}\\) er \\(\\vec{a}\\times\\vec{b}=\\begin{pmatrix}42\\\\27\\\\36\\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-pane3208_689eab-c2\"><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\">PM4-489<\/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\">Arealet af det udsp\u00e6ndte parallelogram er 72.<\/p>\n<\/div><\/div><\/div>\n\n\n\n<div class=\"wp-block-kadence-pane kt-accordion-pane kt-accordion-pane-3 kt-pane3208_a1aae6-5f\"><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\">PM4-490<\/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-id3208_e6406c-24 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-pane3208_73cdaa-e0\"><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\">Vektorproduktet er \\(\\vec{a}\\times\\vec{b}=\\begin{pmatrix}-54\\\\69\\\\60\\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-pane3208_f3dc3a-c7\"><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\">Arealet af det udsp\u00e6ndte parallelogram 106,2.<\/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>Ogs\u00e5 kaldet krydsprudukt, er en m\u00e5de man kan \u201cgange\u201d vektorer sammen lige som skalarproduktet. Hvor skalarproduktet g\u00e6lder for b\u00e5de vektorer i planet og i rummet og giver et tal, der af navnet, g\u00e6lder vektorproduktet kun for vektorer i rummet og giver endnu en tredje vektor som st\u00e5r vinkelret p\u00e5 begge de to vektorer som blev krydset sammen.<\/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-3208","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\/3208","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=3208"}],"version-history":[{"count":6,"href":"https:\/\/mxth.dk\/index.php?rest_route=\/wp\/v2\/posts\/3208\/revisions"}],"predecessor-version":[{"id":3293,"href":"https:\/\/mxth.dk\/index.php?rest_route=\/wp\/v2\/posts\/3208\/revisions\/3293"}],"wp:attachment":[{"href":"https:\/\/mxth.dk\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=3208"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/mxth.dk\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=3208"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/mxth.dk\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=3208"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}