[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki47\/archives\/14996#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/all2jp\/wiki47\/archives\/14996","headline":"\u6df7\u5408\u88fd\u54c1 – \u30a6\u30a3\u30ad\u30da\u30c7\u30a3\u30a2\u3001\u7121\u6599\u200b\u200b\u767e\u79d1\u4e8b\u5178","name":"\u6df7\u5408\u88fd\u54c1 – \u30a6\u30a3\u30ad\u30da\u30c7\u30a3\u30a2\u3001\u7121\u6599\u200b\u200b\u767e\u79d1\u4e8b\u5178","description":"\u6df7\u5408\u88fd\u54c1 – \u4ed6\u306e2\u3064\u306e\u30d9\u30af\u30c8\u30eb\u7a4d\u306b\u3088\u3063\u3066\u305d\u308c\u3089\u306e1\u3064\u306e\u30b9\u30ab\u30e9\u30fc\u7a4d\u3068\u3057\u3066\u30013\u6b21\u5143\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u7a7a\u9593\u306e3\u3064\u306e\u30d9\u30af\u30c8\u30eb\u306b\u5bfe\u3057\u3066\u6307\u5b9a\u3055\u308c\u305f\u30a2\u30af\u30b7\u30e7\u30f3\u3002\u3060\u304b\u3089 a \u3001 b \u3001 c {displaystyle mathbf {a}\u3001mathbf {b}\u3001mathbf {c}} \u305d\u308c\u3089\u306f\u4efb\u610f\u306e\u30d9\u30af\u30c8\u30eb\u3067\u3059 R3\u3001 {displaystyle mathbb {r} ^{3}\u3001} \u6b21\u306e\u5f62\u3067\u3042\u308b\u306e\u306f\u5f7c\u3089\u306e\u6df7\u5408\u88fd\u54c1\u3067\u3059","datePublished":"2021-04-15","dateModified":"2021-04-15","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki47\/archives\/author\/lordneo#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/all2jp\/wiki47\/archives\/author\/lordneo","image":{"@type":"ImageObject","@id":"https:\/\/secure.gravatar.com\/avatar\/44a4cee54c4c053e967fe3e7d054edd4?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/44a4cee54c4c053e967fe3e7d054edd4?s=96&d=mm&r=g","height":96,"width":96}},"publisher":{"@type":"Organization","name":"Enzyklop\u00e4die","logo":{"@type":"ImageObject","@id":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","url":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","width":600,"height":60}},"image":{"@type":"ImageObject","@id":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/98735198279ea2237902abe353cfc8156f2eea0b","url":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/98735198279ea2237902abe353cfc8156f2eea0b","height":"","width":""},"url":"https:\/\/wiki.edu.vn\/all2jp\/wiki47\/archives\/14996","wordCount":3715,"articleBody":"\u6df7\u5408\u88fd\u54c1  – \u4ed6\u306e2\u3064\u306e\u30d9\u30af\u30c8\u30eb\u7a4d\u306b\u3088\u3063\u3066\u305d\u308c\u3089\u306e1\u3064\u306e\u30b9\u30ab\u30e9\u30fc\u7a4d\u3068\u3057\u3066\u30013\u6b21\u5143\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u7a7a\u9593\u306e3\u3064\u306e\u30d9\u30af\u30c8\u30eb\u306b\u5bfe\u3057\u3066\u6307\u5b9a\u3055\u308c\u305f\u30a2\u30af\u30b7\u30e7\u30f3\u3002\u3060\u304b\u3089 a \u3001 b \u3001 c {displaystyle mathbf {a}\u3001mathbf {b}\u3001mathbf {c}} \u305d\u308c\u3089\u306f\u4efb\u610f\u306e\u30d9\u30af\u30c8\u30eb\u3067\u3059 R3\u3001 {displaystyle mathbb {r} ^{3}\u3001} \u6b21\u306e\u5f62\u3067\u3042\u308b\u306e\u306f\u5f7c\u3089\u306e\u6df7\u5408\u88fd\u54c1\u3067\u3059 \uff08 abc\uff09\uff09 \uff1a= ade \uff08 b\u00d7 c\uff09\uff09 \u3002 {displayStyle\uff08mathbf {a}; mathbf {b}; mathbf {c}\uff09\uff1a= mathbf {a} cdot\uff08mathbf {b} times mathbf {c}\uff09\u3002}} \u30a2\u30a4\u30c7\u30f3\u30c6\u30a3\u30c6\u30a3\u304c\u3042\u308b\u304b\u3089\u3067\u3059 ade \uff08 b\u00d7 c\uff09\uff09 = bde \uff08 c\u00d7 a\uff09\uff09 = cde \uff08 a\u00d7 b\uff09\uff09 \u3001 {displaystyle mathbf {a} cdot\uff08mathbf {b}\uff08c}\uff09= mathbf {b} cdot\uff08mathbf {c {c {c {c {c}\uff09= mathbf {c} cdot\uff08mathbf {a} mathbf {b}\u3001} \u3057\u305f\u304c\u3063\u3066\u3001\u4e0a\u8a18\u306e3\u3064\u306e\u5f0f\u306e\u305d\u308c\u305e\u308c\u306f\u3001\u6df7\u5408\u88fd\u54c1\u306e\u5b9a\u7fa9\u3067\u4f7f\u7528\u3067\u304d\u307e\u3059 [\u521d\u3081] \u3002 \u30b7\u30f3\u30dc\u30eb\u3092\u4f7f\u7528\u3057\u3066\u3001\u30ec\u30d3\u30a8\u30b4\u30b5\u30a4\u30c1\u30c3\u30af\u306e\u6df7\u5408\u88fd\u54c1\u306f\u3001\u30d1\u30bf\u30fc\u30f3\u306b\u3088\u3063\u3066\u6c7a\u5b9a\u3067\u304d\u307e\u3059\uff08\u30a2\u30a4\u30f3\u30b7\u30e5\u30bf\u30a4\u30f3\u306e\u8981\u7d04\u6761\u7d04\uff09 \uff08 abc\uff09\uff09 = \u03b5ijkaibjck\u3002 {displaystyle\uff08mathbf {a}; mathbf {b}; mathbf {c}\uff09= varepsilon _ {ijk} a^{i} b^{j} c^{k}\u3002}  \u30de\u30fc\u30af\u3055\u308c\u305f\u9069\u5207\u306a\u30d9\u30af\u30c8\u30eb\u304a\u3088\u3073\u6df7\u5408\u88fd\u54c1\u3068\u4e26\u5217\u3092\u6307\u5b9a\u3059\u308b3\u3064\u306e\u30d9\u30af\u30c8\u30eb\u3002  \u53c2\u7167\uff1a\u65b9\u5411\u3068\u6c7a\u5b9a\u8981\u56e0\u3002 \u7a4d\u6975\u7684\u306b\u914d\u5411\u3055\u308c\u305f\u5ea7\u6a19\u7cfb\u3067\u306f\u3001\u6df7\u5408\u88fd\u54c1\u306f\u30013\u3064\u306e\u30d9\u30af\u30c8\u30eb\u306b\u3088\u3063\u3066\u4f38\u3073\u305f\u4e26\u5217\u6027\u306e\u91cf\u3092\u8aac\u660e\u3057\u3066\u3044\u307e\u3059\u3002\u7a7a\u9593\u306e\u65b9\u5411\u304c\u8ab2\u3055\u308c\u306a\u3044\u5834\u5408\u3001\u524d\u8ff0\u306e\u30dc\u30ea\u30e5\u30fc\u30e0\u306f\u3001\u30d9\u30af\u30bf\u30fc\u306e\u9806\u5e8f\uff08\u9806\u5217\u306e\u7dca\u6025\u4e8b\u614b\uff09\u306b\u4f9d\u5b58\u3059\u308b\u3068\u3044\u3046\u610f\u5473\u3067\u3082\u5411\u3051\u3089\u308c\u307e\u3059\u3002\u65b9\u5411\u3092\u5909\u66f4\u3059\u308b\u3068\u3001\u88fd\u54c1\u306e\u88fd\u54c1\u304c\u5909\u5316\u3059\u308b\u305f\u3081\u3001\u6df7\u5408\u88fd\u54c1\u306f\u30b9\u30ab\u30e9\u30fc\u3067\u306f\u306a\u304f\u3001\u64ec\u4f3c\u30de\u30c6\u30ca\u30ea\u30fc\u3067\u3059\uff08\u30d9\u30af\u30bf\u30fc\u88fd\u54c1\u306f\u64ec\u4f3c\u4eba\u3067\u3042\u308a\u30012\u3064\u306e\u30d9\u30af\u30c8\u30eb\u306e\u30b9\u30ab\u30e9\u30fc\u7523\u7269\u306f\u30b9\u30ab\u30e9\u30fc\u3067\u3059\u304c\u3001\u64ec\u4f3c\u9ebb\u75fa\u8005\u3068\u30d9\u30af\u30bf\u30fc\u306e\u64ec\u4f3c – \u4e00\u898b\u3057\u3066\u304f\u3060\u3055\u3044\uff09\u3002\u307e\u305f\u3001\u30d9\u30af\u30c8\u30eb\u88fd\u54c1\u306e\u30d9\u30af\u30c8\u30eb\u306e\u9806\u5e8f\u306e\u5909\u5316\u306f\u3001\u6df7\u5408\u88fd\u54c1\u306e\u5146\u5019\u3092\u5909\u66f4\u3059\u308b\u3053\u3068\u306b\u306a\u308a\u307e\u3059\uff08\u30b9\u30ab\u30e9\u30fc\u88fd\u54c1\u306f\u4ea4\u4e92\u306b\u3001\u6df7\u5408\u88fd\u54c1\u306e\u5146\u5019\u306b\u5f71\u97ff\u3057\u307e\u305b\u3093\uff09\u3001 \uff08 abc\uff09\uff09 = ade \uff08 b\u00d7 c\uff09\uff09 =  –  ade \uff08 c\u00d7 b\uff09\uff09 =  –  \uff08 acb\uff09\uff09 \u3002 {displaystyle\uff08mathbf {a}; mathbf {b}; mathbf {c}\uff09= mathbf {a} cdot\uff08mathbf {b} times mathbf {c}\uff09= -mathbf {a} cdot\uff08mathbf {c} times mathbf {b {c w {b {bid-cbf {c }; \u6df7\u5408\u88fd\u54c1\u306f\u3082\u30461\u3064\u306e\u6c7a\u5b9a\u3068\u3057\u3066\u6271\u3046\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u30023\u3064\u306e\u30d9\u30af\u30c8\u30eb\u306e\u6df7\u5408\u7a4d\u306f\u30013\u756a\u76ee\u306e\u30de\u30c8\u30ea\u30c3\u30af\u30b9\u306e3\u756a\u76ee\u306e\u30de\u30c8\u30ea\u30c3\u30af\u30b9\u306e\u6c7a\u5b9a\u8981\u56e0\u307e\u305f\u306f\u6c7a\u5b9a\u8981\u56e0\u306b\u7b49\u3057\u304f\u3001\u8a69\u307e\u305f\u306f\u5217\u306b\u8a18\u8ff0\u3055\u308c\u305f\u30d9\u30af\u30c8\u30eb\u3092\u4f7f\u7528\u3057\u3066\uff08\u30de\u30c8\u30ea\u30c3\u30af\u30b9\u3092\u8ee2\u7f6e\u3057\u3066\u3082\u3001\u6c7a\u5b9a\u5264\u304c\u5909\u5316\u3057\u307e\u305b\u3093\uff09\u3001 \uff08 abc\uff09\uff09 =  \uff08 a\u3001 b\u3001 c\uff09\uff09 =  [a1a2a3b1b2b3c1c2c3]\u3001 {displaystyle\uff08mathbf {a}; mathbf {b}; mathbf {c}\uff09= det\uff08mathbf {a}\u3001mathbf {b}\u3001mathbf {c} = det {begin {bmatrix} a_ {1}\uff06a_ {{{2} {2} {2} {2} {2}\u3002{1}\uff06c_ {2}\uff06c_ {3} end {bmatrix}}\u3001} \u3069\u3053 \u30d0\u30c4 = \uff08 \u30d0\u30c4 1\u3001 \u30d0\u30c4 2\u3001 \u30d0\u30c4 3\uff09\uff09 ; {displaystyle mathbf {x} =\uff08x_ {1}\u3001x_ {2}\u3001x_ {3}\uff09;} \u3053\u306e\u30b5\u30a4\u30ba\u306f\u3001\u58f2\u4e0a\u9ad8\u306e\u305f\u3081\u306b\u5909\u66f4\u3055\u308c\u307e\u305b\u3093\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u6df7\u5408\u88fd\u54c1\u306b\u306f\u3001\u591a\u7dda\u6027\u3068\u4ea4\u4e92\u306e\u4ea4\u4e92\u3092\u542b\u3080\u3001\u6c7a\u5b9a\u8981\u56e0\u306e\u3059\u3079\u3066\u306e\u7279\u6027\u304c\u3042\u308a\u307e\u3059\u3002\u3057\u305f\u304c\u3063\u3066\u3001\u305d\u308c\u306f\u6b63\u898f\u5316\u3055\u308c\u305f\u30d5\u30a9\u30fc\u30e0\u306e\u30dc\u30ea\u30e5\u30fc\u30e0\u3067\u3059\u3002 \u30d9\u30af\u30c8\u30eb a \u3001 b \u3001 c {displaystyle mathbf {a}\u3001mathbf {b}\u3001mathbf {c}} \u300c\u30d1\u30e9\u30ec\u30eb\u300d\u304c\u30d5\u30e9\u30c3\u30c8\uff08\u5909\u6027\uff09\u3067\u6307\u5b9a\u3055\u308c\u3066\u304a\u308a\u3001\u30dc\u30ea\u30e5\u30fc\u30e0\u304c\u306a\u3044\u305f\u3081\u3001\u88fd\u54c1\u304c\u30bc\u30ed\u3068\u6df7\u5408\u3055\u308c\u3066\u3044\u308b\u5834\u5408\u306b\u306e\u307f\u3001\u5171\u540c\u30d1\u30f3\u30c6\u30a3\u3067\u3059\u3002\u52a0\u3048\u3066 |\uff08 abc\uff09\uff09 |\u2a7d |a||b||c|\u3002 {displaystyle {big |}\uff08mathbf {a}; mathbf {b}; mathbf {c}\uff09{big |} leqslant | mathbf {a} || mathbf {b} || mathbf {c} |\u3002}} \u6b21\u306e\u6240\u6709\u6a29\u3082\u884c\u308f\u308c\u307e\u3059\u3002 \uff08 abc\uff09\uff09 a= \uff08 a\u00d7 b\uff09\uff09 \u00d7 \uff08 a\u00d7 c\uff09\uff09 \u3002 {displaystyle\uff08mathbf {a}; mathbf {b}; mathbf {c}\uff09mathbf {a} =\uff08mathbf {a} mathbf {b}\uff09times\uff08mathbf {a} times mathbf {c}\uff09\u3002}}  \u5225\u3005\u306e\u8a18\u4e8b\uff1a\u5916\u90e8\u4ee3\u6570\u3068\u5e7e\u4f55\u5b66\u7684\u4ee3\u6570\u3002  \u5916\u90e8\u304a\u3088\u3073\u5e7e\u4f55\u4ee3\u6570\u3067\u306f\u30012\u3064\u306e\u30d9\u30af\u30c8\u30eb\u306e\u5916\u5074\u7a4d\u306f2\u3064\u306e\u7dda\u3001\u3064\u307e\u308a\u5e73\u9762\u306e\u914d\u5411\u8981\u7d20\u3067\u3042\u308a\u30013\u3064\u306e\u30d9\u30af\u30c8\u30eb\u306e\u5916\u5074\u7a4d\u306f\u30c8\u30ea\u30ac\u30fc\u3001\u3064\u307e\u308a\u4f53\u7a4d\u306e\u914d\u5411\u8981\u7d20\u3067\u3059\u3002\u3053\u308c\u3089\u306f\u3001\u6307\u5411\u306e\u76f4\u7dda\u8981\u7d20\u3068\u3057\u3066\u306e\u30d9\u30af\u30c8\u30eb\u306e\u81ea\u7136\u306a\u4e00\u822c\u5316\u3067\u3059\u3002\u30d9\u30af\u30c8\u30eb\u30c7\u30fc\u30bf\u306e\u5834\u5408 a \u3001 b \u3001 c {displaystyle mathbf {a}\u3001mathbf {b}\u3001mathbf {c}} \u5f7c\u3089\u306e\u5916\u90e8\u88fd\u54c1 a\u2227 b\u2227 c{displaystyle mathbf {a}\u30a6\u30a7\u30c3\u30b8Mathbf {b}\u30a6\u30a7\u30c3\u30b8Mathbf {c}} \u5f7c\u306f3\u3064\u306e\u6709\u7dda\u6c34\u3067\u3059\u3002\u3064\u307e\u308a\u3001\u6df7\u5408\u88fd\u54c1\u306b\u7b49\u3057\u3044\u5024\u3092\u6301\u3064\u3001\u6df7\u5408\u88fd\u54c1\u306e\u4e8c\u91cd\u306e\u64ec\u4f3c\u30b5\u30e9\u30fc\u3067\u3059\uff08\u5916\u90e8\u88fd\u54c1\u304c\u7d44\u307f\u5408\u308f\u3055\u308c\u3066\u3044\u308b\u305f\u3081\u3001\u62ec\u5f27\u306f\u7701\u7565\u3055\u308c\u307e\u3059\u304c\u3001\u4ee3\u66ff\u3067\u306f\u3042\u308a\u307e\u305b\u3093\uff09\u3002 3\u3064\u306e\u30e9\u30a4\u30f3 a \u2227 b \u2227 c {displaystyle mathbf {a}\u30a6\u30a7\u30c3\u30b8Mathbf {b}\u30a6\u30a7\u30c3\u30b8Mathbf {c}} \u30d9\u30af\u30c8\u30eb\u3068\u306e\u5e73\u884c\u306b\u5bfe\u5fdc\u3057\u307e\u3059 a \u3001 b \u3001 c \u3001 {displaystyle mathbf {a}\u3001mathbf {b}\u3001mathbf {c}\u3001} \u3053\u3053\u3067\u30012\u3064\u306e\u30a6\u30a7\u30af\u30bf\u30fc a \u2227 b \u3001 b \u2227 c \u3001 a \u2227 c {displaystyle mathbf {a}\u30a6\u30a7\u30c3\u30b8Mathbf {b}\u3001; mathbf {b}\u30a6\u30a7\u30c3\u30b8Mathbf {c}\u3001; mathbf {a}\u30a6\u30a7\u30c3\u30b8Mathbf {c}} \u5e73\u884c\u3057\u305f\u5e73\u884c\u58c1\u306e\u58c1\u306f\u5bfe\u5fdc\u3057\u307e\u3059\u3002   "},{"@context":"http:\/\/schema.org\/","@type":"BreadcrumbList","itemListElement":[{"@type":"ListItem","position":1,"item":{"@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki47\/#breadcrumbitem","name":"Enzyklop\u00e4die"}},{"@type":"ListItem","position":2,"item":{"@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki47\/archives\/14996#breadcrumbitem","name":"\u6df7\u5408\u88fd\u54c1 – \u30a6\u30a3\u30ad\u30da\u30c7\u30a3\u30a2\u3001\u7121\u6599\u200b\u200b\u767e\u79d1\u4e8b\u5178"}}]}]