\u3000\u30d9\u30af\u30c8\u30eb $\\bold{A}$ \u3068\u30d9\u30af\u30c8\u30eb $\\bold{B}$ \u3068\u306e\u30af\u30ed\u30b9\u7a4d\u307e\u305f\u306f\u30d9\u30af\u30c8\u30eb\u7a4d\u306f $\\bold{C} = \\bold{A} \\times \\bold{B}$ \u3068\u8a18\u8ff0\u3057 $\\bold{A}$ \u30af\u30ed\u30b9 $\\bold{B}$ \u3068\u8aad\u307f\u307e\u3059\uff0e $\\bold{A}\\times\\bold{B}$ \u306e\u5927\u304d\u3055\u306f $\\bold{A}$ \u304a\u3088\u3073 $\\bold{B}$ \u306e\u5927\u304d\u3055\u3068\u4e21\u8005\u306e\u306a\u3059\u89d2\u306e\u30b5\u30a4\u30f3\u3068\u306e\u7a4d\u3068\u5b9a\u7fa9\u3055\u308c\u307e\u3059\uff0e\u30d9\u30af\u30c8\u30eb $\\bold{C} = \\bold{A}\\times\\bold{B}$ \u306e\u65b9\u5411\u306f $\\bold{A}$ \u304a\u3088\u3073 $\\bold{B}$ \u306e\u306a\u3059\u5e73\u9762\u3068\u5782\u76f4\u3067\u3042\u308a\uff0c\u305d\u306e\u3088\u3046\u306a\u30d9\u30af\u30c8\u30eb $\\bold{A}$ , $\\bold{B}$ \u304a\u3088\u3073 $\\bold{C}$ \u306f\u53f3\u624b\u7cfb\u3092\u5f62\u6210\u3057\u307e\u3059\uff0e\u8a18\u53f7\u3067\u306f\u4e0b\u8a18\u306e\u3088\u3046\u306b\u8a18\u3057\u307e\u3059\uff0e<\/p>\n

$\\bold{A}\\times\\bold{B} = AB\\sin{\\theta}\\bold{u},\\ 0\\le\\theta\\le\\pi\\cdots(5)$ <\/p>\n

\u3053\u3053\u3067 $\\bold{u}$ \u306f $\\bold{A}\\times\\bold{B}$ \u306e\u65b9\u5411\u3092\u6307\u3059\u5358\u4f4d\u30d9\u30af\u30c8\u30eb\u3067\u3059\uff0e\u4eee\u306b $\\bold{A} = \\bold{B}$ \u307e\u305f\u306f $\\bold{A}$ \u304c $\\bold{B}$ \u306b\u5bfe\u3057\u3066\u5e73\u884c\u306e\u5834\u5408\uff0c $\\sin\\theta = 0$ \u3068\u306a\u3063\u3066 $\\bold{A}\\times\\bold{B} = 0$ \u3068\u5b9a\u7fa9\u3067\u304d\u307e\u3059\uff0e<\/p>\n

\"\/\/en.wikipedia.org\/wiki\/Vector_product\" — \/\/en.wikipedia.org\/wiki\/Vector_product<\/figcaption><\/figure>\n
\u3000\u4e0b\u8a18\u306e\u6cd5\u5247\u304c\u6709\u52b9\u3067\u3059\uff0e<\/p>\n
\n
$\\bold{A} \\times \\bold{B} = - \\bold{B} \\times \\bold{A}$ <\/li>\n
$\\bold{A} \\times (\\bold{B} + \\bold{C}) = \\bold{A}\\times\\bold{B} + \\bold{A} \\times \\bold{C}$ <\/li>\n
$m( \\bold{A} \\times \\bold{B}) = (m \\bold{A}) \\times \\bold{B} = \\bold{A} \\times (m \\bold{B}) = (\\bold{A} \\times \\bold{B})m$ <\/li>\n
$\\bold{i} \\times \\bold{i} = \\bold{j} \\times \\bold{j} = \\bold{k} \\times \\bold{k} = 0,\\ \\bold{i} \\times \\bold{j} = \\bold{k},\\ \\bold{j} \\times \\bold{k} = \\bold{i},\\ \\bold{k} \\times \\bold{i} = \\bold{j}$ <\/li>\n
\u4eee\u306b $\\bold{A} = A_1\\bold{i} + A_2\\bold{j} + A_3\\bold{k}$ \u307e\u305f $\\bold{B} = B_1\\bold{i} + B_2\\bold{j} + B_3\\bold{k}$ \u306e\u5834\u5408\uff0c<\/li>\n
$\\displaystyle \\bold{A} \\times \\bold{B} = \\left|\\begin{array}{ccc} \\bold{i} & \\bold{j} & \\bold{k} \\\\ A_1 & A_2 & A_3 \\\\ B_1 & B_2 & B_3 \\end{array}\\right| = \\left|\\begin{array}{cc} A_2 & A_3 \\\\ B_2 & B_3 \\end{array}\\right| \\bold{i} - \\left|\\begin{array}{cc} A_1 & A_3 \\\\ B_1 & B_3 \\end{array}\\right| \\bold{j} + \\left|\\begin{array}{cc} A_1 & A_2 \\\\ B_1 & B_2 \\end{array}\\right| \\bold{k}$ <\/p>\n
$|\\bold{A} \\times \\bold{B}|$ \u306f $\\bold{A}$ \u304a\u3088\u3073 $\\bold{B}$ \u304c\u8fba\u3068\u306a\u308b\u5e73\u884c\u56db\u8fba\u5f62\u306e\u9762\u7a4d\u3092\u8868\u3057\u307e\u3059\uff0e<\/li>\n
\u4eee\u306b $\\bold{A} \\times \\bold{B} = 0$ \u3067\u3042\u3063\u3066 $\\bold{A}$ \u304a\u3088\u3073 $\\bold{B}$ \u304c\u96f6\u30d9\u30af\u30c8\u30eb\u3067\u306a\u3044\u5834\u5408\uff0c $\\bold{A}$ \u304a\u3088\u3073 $\\bold{B}$ \u306f\u5e73\u884c\u3068\u306a\u308a\u307e\u3059\uff0e<\/li>\n<\/ol>\n
\u3000\u30af\u30ed\u30b9\u7a4d\u306b\u304a\u3044\u3066\u306f\u4ea4\u63db\u6cd5\u5247\u304c\u6210\u308a\u7acb\u305f\u306a\u3044\u3053\u3068\u306b\u6ce8\u610f\u304c\u5fc5\u8981\u3067\u3059\uff0e<\/p>\n
<\/iframe><\/p>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>\u3000\u30d9\u30af\u30c8\u30eb \u3068\u30d9\u30af\u30c8\u30eb \u3068\u306e\u30af\u30ed\u30b9\u7a4d\u307e\u305f\u306f\u30d9\u30af\u30c8\u30eb\u7a4d\u306f \u3068\u8a18\u8ff0\u3057 \u30af\u30ed\u30b9 \u3068\u8aad\u307f\u307e\u3059\uff0e \u306e\u5927\u304d\u3055\u306f \u304a\u3088\u3073 \u306e\u5927\u304d\u3055\u3068\u4e21\u8005\u306e\u306a\u3059\u89d2\u306e\u30b5\u30a4\u30f3\u3068\u306e\u7a4d\u3068\u5b9a\u7fa9\u3055\u308c\u307e\u3059\uff0e\u30d9\u30af\u30c8\u30eb \u306e\u65b9\u5411\u306f \u304a\u3088\u3073 \u306e\u306a\u3059\u5e73\u9762\u3068\u5782\u76f4\u3067\u3042\u308a\uff0c\u305d\u306e\u3088\u3046 … <a href=\"https:\/\/www.fujiitoshiki.com\/improvesociety\/?p=4966\" class=\"more-link\"><span class=\"screen-reader-text\">“\u30af\u30ed\u30b9\u7a4d\u307e\u305f\u306f\u30d9\u30af\u30c8\u30eb\u7a4d” \u306e<\/span>\u7d9a\u304d\u3092\u8aad\u3080<\/a><\/p>\n","protected":false},"author":1,"featured_media":6040,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_crdt_document":"","_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"categories":[9],"tags":[],"class_list":["post-4966","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mathematics"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/posts\/4966","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=4966"}],"version-history":[{"count":16,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/posts\/4966\/revisions"}],"predecessor-version":[{"id":6784,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/posts\/4966\/revisions\/6784"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/media\/6040"}],"wp:attachment":[{"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=4966"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=4966"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=4966"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}

\/\/en.wikipedia.org\/wiki\/Vector_product<\/figcaption><\/figure>\n
\u3000\u4e0b\u8a18\u306e\u6cd5\u5247\u304c\u6709\u52b9\u3067\u3059\uff0e<\/p>\n
\n
$\\bold{A} \\times \\bold{B} = - \\bold{B} \\times \\bold{A}$ <\/li>\n
$\\bold{A} \\times (\\bold{B} + \\bold{C}) = \\bold{A}\\times\\bold{B} + \\bold{A} \\times \\bold{C}$ <\/li>\n
$m( \\bold{A} \\times \\bold{B}) = (m \\bold{A}) \\times \\bold{B} = \\bold{A} \\times (m \\bold{B}) = (\\bold{A} \\times \\bold{B})m$ <\/li>\n
$\\bold{i} \\times \\bold{i} = \\bold{j} \\times \\bold{j} = \\bold{k} \\times \\bold{k} = 0,\\ \\bold{i} \\times \\bold{j} = \\bold{k},\\ \\bold{j} \\times \\bold{k} = \\bold{i},\\ \\bold{k} \\times \\bold{i} = \\bold{j}$ <\/li>\n
\u4eee\u306b $\\bold{A} = A_1\\bold{i} + A_2\\bold{j} + A_3\\bold{k}$ \u307e\u305f $\\bold{B} = B_1\\bold{i} + B_2\\bold{j} + B_3\\bold{k}$ \u306e\u5834\u5408\uff0c<\/li>\n
$\\displaystyle \\bold{A} \\times \\bold{B} = \\left|\\begin{array}{ccc} \\bold{i} & \\bold{j} & \\bold{k} \\\\ A_1 & A_2 & A_3 \\\\ B_1 & B_2 & B_3 \\end{array}\\right| = \\left|\\begin{array}{cc} A_2 & A_3 \\\\ B_2 & B_3 \\end{array}\\right| \\bold{i} - \\left|\\begin{array}{cc} A_1 & A_3 \\\\ B_1 & B_3 \\end{array}\\right| \\bold{j} + \\left|\\begin{array}{cc} A_1 & A_2 \\\\ B_1 & B_2 \\end{array}\\right| \\bold{k}$ <\/p>\n
$|\\bold{A} \\times \\bold{B}|$ \u306f $\\bold{A}$ \u304a\u3088\u3073 $\\bold{B}$ \u304c\u8fba\u3068\u306a\u308b\u5e73\u884c\u56db\u8fba\u5f62\u306e\u9762\u7a4d\u3092\u8868\u3057\u307e\u3059\uff0e<\/li>\n
\u4eee\u306b $\\bold{A} \\times \\bold{B} = 0$ \u3067\u3042\u3063\u3066 $\\bold{A}$ \u304a\u3088\u3073 $\\bold{B}$ \u304c\u96f6\u30d9\u30af\u30c8\u30eb\u3067\u306a\u3044\u5834\u5408\uff0c $\\bold{A}$ \u304a\u3088\u3073 $\\bold{B}$ \u306f\u5e73\u884c\u3068\u306a\u308a\u307e\u3059\uff0e<\/li>\n<\/ol>\n
\u3000\u30af\u30ed\u30b9\u7a4d\u306b\u304a\u3044\u3066\u306f\u4ea4\u63db\u6cd5\u5247\u304c\u6210\u308a\u7acb\u305f\u306a\u3044\u3053\u3068\u306b\u6ce8\u610f\u304c\u5fc5\u8981\u3067\u3059\uff0e<\/p>\n
<\/iframe><\/p>\n<\/div>","protected":false},"excerpt":{"rendered":"<p>\u3000\u30d9\u30af\u30c8\u30eb \u3068\u30d9\u30af\u30c8\u30eb \u3068\u306e\u30af\u30ed\u30b9\u7a4d\u307e\u305f\u306f\u30d9\u30af\u30c8\u30eb\u7a4d\u306f \u3068\u8a18\u8ff0\u3057 \u30af\u30ed\u30b9 \u3068\u8aad\u307f\u307e\u3059\uff0e \u306e\u5927\u304d\u3055\u306f \u304a\u3088\u3073 \u306e\u5927\u304d\u3055\u3068\u4e21\u8005\u306e\u306a\u3059\u89d2\u306e\u30b5\u30a4\u30f3\u3068\u306e\u7a4d\u3068\u5b9a\u7fa9\u3055\u308c\u307e\u3059\uff0e\u30d9\u30af\u30c8\u30eb \u306e\u65b9\u5411\u306f \u304a\u3088\u3073 \u306e\u306a\u3059\u5e73\u9762\u3068\u5782\u76f4\u3067\u3042\u308a\uff0c\u305d\u306e\u3088\u3046 … <a href=\"https:\/\/www.fujiitoshiki.com\/improvesociety\/?p=4966\" class=\"more-link\"><span class=\"screen-reader-text\">“\u30af\u30ed\u30b9\u7a4d\u307e\u305f\u306f\u30d9\u30af\u30c8\u30eb\u7a4d” \u306e<\/span>\u7d9a\u304d\u3092\u8aad\u3080<\/a><\/p>\n","protected":false},"author":1,"featured_media":6040,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"_crdt_document":"","_monsterinsights_skip_tracking":false,"_monsterinsights_sitenote_active":false,"_monsterinsights_sitenote_note":"","_monsterinsights_sitenote_category":0,"footnotes":""},"categories":[9],"tags":[],"class_list":["post-4966","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-mathematics"],"aioseo_notices":[],"_links":{"self":[{"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/posts\/4966","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=4966"}],"version-history":[{"count":16,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/posts\/4966\/revisions"}],"predecessor-version":[{"id":6784,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/posts\/4966\/revisions\/6784"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=\/wp\/v2\/media\/6040"}],"wp:attachment":[{"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=4966"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=4966"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.fujiitoshiki.com\/improvesociety\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=4966"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}