{"id":727,"date":"2025-12-24T17:22:58","date_gmt":"2025-12-24T08:22:58","guid":{"rendered":"https:\/\/math-travel.com\/?p=727"},"modified":"2026-03-06T01:12:59","modified_gmt":"2026-03-05T16:12:59","slug":"vector-length","status":"publish","type":"post","link":"https:\/\/math-travel.jp\/math-b\/vector-length\/","title":{"rendered":"\u30d9\u30af\u30c8\u30eb\u306e\u5927\u304d\u3055\u306e\u6c42\u3081\u65b9\uff1a\u306a\u305c\u300c2\u4e57\u3057\u3066\u5185\u7a4d\u300d\u3092\u4f7f\u3046\u306e\u304b\u7406\u7531\u3068\u8a08\u7b97\u306e\u30b3\u30c4"},"content":{"rendered":"\n
\u300c\u7b49\u3057\u3044\u30d9\u30af\u30c8\u30eb\u3068\u306f\uff1f\u300d <\/p>\n\n\n\n
\u300c\u30d9\u30af\u30c8\u30eb\u306e\u5927\u304d\u3055\u3063\u3066\uff1f\u300d<\/p>\n<\/div><\/div>\n\n\n\n
\u30d9\u30af\u30c8\u30eb\u306e\u201d\u5927\u304d\u3055”\u3068\u306f\u9577\u3055\u3092\u8868\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n
\u5927\u304d\u3055\u306e\u6c42\u3081\u65b9\u306f\u7c21\u5358\u306a\u306e\u3067\u5fc5\u305a\u62bc\u3055\u3048\u3066\u304a\u304d\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n
\u672c\u8a18\u4e8b\u3067\u306f\u3001\u30d9\u30af\u30c8\u30eb\u306e\u5927\u304d\u3055\u3092\u6c42\u3081\u308b\u516c\u5f0f<\/span>\u3092\u89e3\u8aac\u3057\u3066\u3044\u307e\u3059\u3002<\/p>\n\n\n\n \u4e0b\u56f3\u306e\u3088\u3046\u306a\u5927\u304d\u3055\u3068\u5411\u304d\u3067\u5b9a\u307e\u308b\u3082\u306e\u3092\u30d9\u30af\u30c8\u30eb<\/span>\u3068\u3044\u3044\u307e\u3059\u3002<\/p>\n\n\n \u6709\u5411\u7dda\u5206AB\u3067\u8868\u3055\u308c\u308b\u30d9\u30af\u30c8\u30eb\u3092\u3001\\(\\overrightarrow{ AB }\\)\u3068\u66f8\u304d\u8868\u3059\u3002<\/p>\n\n\n\n \u3053\u306e\u3068\u304d\u3001\u7dda\u5206AB\u306e\u9577\u3055\u3092\u30d9\u30af\u30c8\u30ebAB\u306e“\u5927\u304d\u3055”<\/span>\u3068\u3057\u3066\\(|\\overrightarrow{ AB }|\\)\u3068\u8868\u3057\u307e\u3059\u3002<\/p>\n\n\n\n \u5e73\u9762\u30d9\u30af\u30c8\u30eb\u306e\u5927\u304d\u3055\u306e\u6c42\u3081\u65b9\u3092\u7d39\u4ecb\u3057\u307e\u3059\u3002<\/span><\/p>\n\n\n\n \\(\\vec{AB} = (x, y)\\)\u306e\u5927\u304d\u3055\\(|\\overrightarrow{ AB }|\\)\u306f\u3001<\/p>\n\n\n\n \\[|\\overrightarrow{ AB }|=\\sqrt{x^2 + y^2}\\]<\/p>\n<\/div><\/div>\n\n\n\n \\(A(0,0),B(3,4)\\)\u3068\u3059\u308b\u3068\\(\\vec{AB} = (3, 4)\\)\u306e\u5927\u304d\u3055\u306f\u3001<\/p>\n\n\n\n \\[|\\overrightarrow{ AB }|=\\sqrt{3^2 + 4^2}=\\sqrt{25}=5\\]<\/p>\n\n\n\n \u3057\u305f\u304c\u3063\u3066\u3001\\(\\vec{AB} = (3, 4)\\)\u306e\u5927\u304d\u3055\u306f5\u3068\u3044\u3046\u3053\u3068\u304c\u5206\u304b\u308a\u307e\u3057\u305f\u3002<\/p>\n\n\n\n \u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u306e\u5834\u5408\u306f\u6210\u5206\u304c3\u3064\u306b\u306a\u308b\u306e\u3067\u3001\u5927\u304d\u3055\u306e\u6c42\u3081\u65b9\u3082\u5909\u308f\u308a\u307e\u3059\u3002<\/span><\/p>\n\n\n\n \\(\\vec{AB} = (x, y, z)\\)\u306e\u5927\u304d\u3055\\(|\\overrightarrow{ AB }|\\)\u306f\u3001<\/p>\n\n\n\n \\[|\\overrightarrow{ AB }|=\\sqrt{x^2 + y^2 +z^2}\\]<\/p>\n<\/div><\/div>\n\n\n\n \\(A(0,0,0),B(3,4,5)\\)\u3068\u3059\u308b\u3068\\(\\vec{AB} = (3, 4,5)\\)\u306e\u5927\u304d\u3055\u306f\u3001<\/p>\n\n\n\n \\[|\\overrightarrow{ AB }|=\\sqrt{3^2 + 4^2 +5^2}=\\sqrt{50}=5\\sqrt{2}\\]<\/p>\n\n\n\n \u3057\u305f\u304c\u3063\u3066\u3001\\(\\vec{AB} = (3, 4 ,5)\\)\u306e\u5927\u304d\u3055\u306f\\(5\\sqrt{2}\\)\u3068\u3044\u3046\u3053\u3068\u304c\u5206\u304b\u308a\u307e\u3057\u305f\u3002<\/p>\n\n\n\n \u5358\u4f4d\u30d9\u30af\u30c8\u30eb\u3068\u306f\u3001\u5927\u304d\u3055\u304c\uff11\u306e\u30d9\u30af\u30c8\u30eb\u3067\u3059\u3002<\/span><\/p>\n\n\n\n \u5358\u4f4d\u30d9\u30af\u30c8\u30eb\u306e\u5177\u4f53\u4f8b\u3092\u898b\u3066\u307f\u307e\u3057\u3087\u3046\u3002<\/p>\n\n\n\n \\(\\displaystyle A(0,0),B(\\frac{3}{5},\\frac{4}{5})\\)\u3068\u3059\u308b\u3068\\(\\displaystyle \\vec{AB} = (\\frac{3}{5}, \\frac{4}{5})\\)\u3067\u3059\u3002<\/p>\n\n\n\n \u3053\u306e\u3068\u304d\\(\\displaystyle \\vec{AB} = (\\frac{3}{5}, \\frac{4}{5})\\)\u306e\u5927\u304d\u3055\u306f\u3001<\/p>\n\n\n\n \\[\\displaystyle |\\overrightarrow{ AB }|=\\sqrt{(\\frac{3}{5})^2 + (\\frac{4}{5})^2}=\\sqrt{\\frac{9}{25} + \\frac{16}{25}}=1\\]<\/p>\n\n\n \u3057\u305f\u304c\u3063\u3066\u3001\\(\\displaystyle \\vec{AB} = (\\frac{3}{5}, \\frac{4}{5})\\)\u306f\u5927\u304d\u3055\u304c1\u306a\u306e\u3067\u5358\u4f4d\u30d9\u30af\u30c8\u30eb\u3067\u3059\u3002<\/p>\n\n\n\n \\(\\vec{a}\u3068\\vec{b}\\)\u306e\u5411\u304d<\/span>\u3068\u5927\u304d\u3055<\/span>\u304c\u7b49\u3057\u3044\u3068\u304d\u3001<\/p>\n\n\n\n \uff12\u3064\u306e\u30d9\u30af\u30c8\u30eb\u306f\u7b49\u3057\u3044<\/span>\u3068\u3044\u3044\u3001\\(\\vec{a}\uff1d\\vec{b}\\)\u3068\u66f8\u304f\u3002<\/p>\n\n\n\n \u5927\u304d\u3055\u3082\u5411\u304d\u3082\u7b49\u3057\u3044\u306e\u3067\u3001\u7b49\u3057\u30442\u3064\u306e\u30d9\u30af\u30c8\u30eb\u306f\u5e73\u884c\u79fb\u52d5\u3059\u308b\u3068\u3074\u3063\u305f\u308a\u3068\u91cd\u306d\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n \u30d9\u30af\u30c8\u30eb\u306e\u5927\u304d\u3055\u306f\u5148\u306b2\u4e57\u3057\u3066\u3001\u3042\u3068\u304b\u30892\u4e57\u3092\u5916\u3059\u6c42\u3081\u65b9\u3082\u3042\u308a\u307e\u3059\u3002<\/p>\n\n\n\n \\(A(0,0),B(3,4)\\)\u3068\u3059\u308b\u3068<\/p>\n\n\n\n \\[|\\overrightarrow{ AB }|^{2}=3^2 + 4^2=25\\]<\/p>\n\n\n\n \\(|\\overrightarrow{ AB }| \\ge 0\\)\u306a\u306e\u3067\u3001<\/p>\n\n\n\n \\[|\\overrightarrow{ AB }|=5\\]<\/p>\n<\/div><\/div>\n\n\n\n \u5148\u307b\u3069\u89e3\u8aac\u3057\u305f\u516c\u5f0f\u3067\u306f\u3001\u30eb\u30fc\u30c8\u3092\u4f7f\u3044\u307e\u3057\u305f\u304c\u3053\u306e\u516c\u5f0f\u3067\u306f\u30eb\u30fc\u30c8\u3092\u5f8c\u56de\u3057\u306b\u3067\u304d\u307e\u3059\u3002<\/p>\n\n\n\n \u4eca\u56de\u306f\u30d9\u30af\u30c8\u30eb\u306e\u5927\u304d\u3055\u306b\u3064\u3044\u3066\u307e\u3068\u3081\u307e\u3057\u305f\u3002<\/p>\n\n\n\n \u5e73\u9762\u30d9\u30af\u30c8\u30eb\u306e\u5927\u304d\u3055\u306e\u6c42\u3081\u65b9<\/span><\/p>\n\n\n\n \\(\\vec{AB} = (x, y)\\)\u306e\u5927\u304d\u3055\\(|\\overrightarrow{ AB }|\\)\u306f\u3001<\/p>\n\n\n\n \\[|\\overrightarrow{ AB }|=\\sqrt{x^2 + y^2}\\]<\/p>\n<\/div><\/div>\n\n\n\n \u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u306e\u5927\u304d\u3055\u306e\u6c42\u3081\u65b9<\/span><\/p>\n\n\n\n \\(\\vec{AB} = (x, y, z)\\)\u306e\u5927\u304d\u3055\\(|\\overrightarrow{ AB }|\\)\u306f\u3001<\/p>\n\n\n\n \\[|\\overrightarrow{ AB }|=\\sqrt{x^2 + y^2 +z^2}\\]<\/p>\n<\/div><\/div>\n\n\n\n \u30d9\u30af\u30c8\u30eb\u304c\u82e6\u624b\u306a\u65b9\u306f\u591a\u3044\u3068\u601d\u3044\u307e\u3059\u304c\u3001\u6163\u308c\u308b\u307e\u3067\u306f\u77e2\u5370\u3060\u3068\u601d\u3048\u3070\u826f\u3044\u3067\u3059\u3002<\/p>\n\n\n\n \u307e\u305a\u306f\u516c\u5f0f\u3092\u3057\u3063\u304b\u308a\u3068\u899a\u3048\u3066\u304b\u3089\u304c\u52dd\u8ca0\u3067\u3059\u3002<\/p>\n\n\n\n \u6559\u79d1\u66f8\u306b\u5185\u5bb9\u306b\u6cbf\u3063\u305f\u89e3\u8aac\u8a18\u4e8b\u3092\u6319\u3052\u3066\u3044\u308b\u306e\u3067\u3001\u5b9a\u671f\u8a66\u9a13\u524d\u306b\u78ba\u8a8d\u3057\u3066\u304f\u3060\u3055\u3044\u3002<\/p>\n\n\n\n \u305d\u308c\u3067\u306f\u6700\u5f8c\u307e\u3067\u3054\u89a7\u3044\u305f\u3060\u304d\u3042\u308a\u304c\u3068\u3046\u3054\u3056\u3044\u307e\u3057\u305f\u3002<\/p>\n\n\n\n \u307f\u3093\u306a\u306e\u52aa\u529b\u304c\u5831\u308f\u308c\u307e\u3059\u3088\u3046\u306b\uff01<\/p>\n","protected":false},"excerpt":{"rendered":" \u30d9\u30af\u30c8\u30eb\u306e\u201d\u5927\u304d\u3055”\u3068\u306f\u9577\u3055\u3092\u8868\u3057\u3066\u3044\u307e\u3059\u3002 \u5927\u304d\u3055\u306e\u6c42\u3081\u65b9\u306f\u7c21\u5358\u306a\u306e\u3067\u5fc5\u305a\u62bc\u3055\u3048\u3066\u304a\u304d\u307e\u3057\u3087\u3046\u3002 \u672c\u8a18\u4e8b\u3067\u306f\u3001\u30d9\u30af\u30c8\u30eb\u306e\u5927\u304d\u3055\u3092\u6c42\u3081\u308b\u516c\u5f0f\u3092\u89e3\u8aac\u3057\u3066\u3044\u307e\u3059\u3002 \u30d9\u30af\u30c8\u30eb\u306e\u5927\u304d\u3055\u3068\u6c42\u3081\u65b9 \u4e0b\u56f3\u306e\u3088\u3046\u306a\u5927\u304d\u3055\u3068\u5411 […]<\/p>\n","protected":false},"author":1,"featured_media":4153,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"swell_btn_cv_data":"","footnotes":""},"categories":[16,225],"tags":[17,14,11],"class_list":["post-727","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-vector","category-math-b","tag-17","tag-b","tag-11"],"yoast_head":"\n\u30d9\u30af\u30c8\u30eb\u306e\u5927\u304d\u3055\u3068\u6c42\u3081\u65b9<\/h2>\n\n\n\n
<\/figure>\n<\/div>\n\n\n\u5e73\u9762\u30d9\u30af\u30c8\u30eb\u306e\u3068\u304d<\/h3>\n\n\n\n
\u7a7a\u9593\u30d9\u30af\u30c8\u30eb\u306e\u3068\u304d<\/h3>\n\n\n\n
\u5358\u4f4d\u30d9\u30af\u30c8\u30eb\u306f\u5927\u304d\u30551<\/h2>\n\n\n\n
<\/figure>\n<\/div>\n\n\n\u5927\u304d\u3055\u306e\u7b49\u3057\u3044\u30d9\u30af\u30c8\u30eb\u3068\u306f\uff1f<\/h2>\n\n\n\n
<\/figure>\n<\/div>\n\n\n\u306a\u305c\u30d9\u30af\u30c8\u30eb\u306e\u5927\u304d\u3055\u306f2\u4e57\uff1f<\/h2>\n\n\n\n
\u30d9\u30af\u30c8\u30eb\u306e\u5927\u304d\u3055\u3000\u307e\u3068\u3081<\/h2>\n\n\n\n