{"id":1110,"date":"2015-06-20T23:15:14","date_gmt":"2015-06-20T14:15:14","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=1110"},"modified":"2025-03-18T01:43:54","modified_gmt":"2025-03-17T16:43:54","slug":"kyr201401","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/kyr201401\/","title":{"rendered":"\u4eac\u5927\u7406\u7cfb2014\uff1a\u7b2c1\u554f"},"content":{"rendered":"<hr \/>\r\n<p>\u5ea7\u6a19\u7a7a\u9593\u306b\u304a\u3051\u308b\u6b21\u306e $3$ \u3064\u306e\u76f4\u7dda $l , m , n$ \u3092\u8003\u3048\u308b\uff1a<\/p>\r\n<ul>\r\n<li>$l$ \u306f\u70b9A $( 1 , 0 , -2 )$ \u3092\u901a\u308a, \u30d9\u30af\u30c8\u30eb $\\overrightarrow{u} = ( 2 , 1 , -1 )$ \u306b\u5e73\u884c\u306a\u76f4\u7dda\u3067\u3042\u308b. <\/li>\r\n<li>$m$ \u306f\u70b9B $( 1 , 2 , -3 )$ \u3092\u901a\u308a, \u30d9\u30af\u30c8\u30eb $\\overrightarrow{v} = ( 1 , -1 , 1 )$ \u306b\u5e73\u884c\u306a\u76f4\u7dda\u3067\u3042\u308b. <\/li>\r\n<li>$n$ \u306f\u70b9C $( 1 , -1 , 0 )$ \u3092\u901a\u308a, \u30d9\u30af\u30c8\u30eb $\\overrightarrow{w} = ( 1 , 2 , 1 )$ \u306b\u5e73\u884c\u306a\u76f4\u7dda\u3067\u3042\u308b. <\/li>\r\n<\/ul>\r\n<p>P \u3092 $l$ \u4e0a\u306e\u70b9\u3068\u3057\u3066, P \u304b\u3089 $m , n$ \u3078\u4e0b\u308d\u3057\u305f\u5782\u7dda\u306e\u8db3\u3092\u305d\u308c\u305e\u308c Q , R \u3068\u3059\u308b. \u3053\u306e\u3068\u304d, $\\text{PQ}^2 +\\text{PR}^2$ \u3092\u6700\u5c0f\u306b\u3059\u308b\u3088\u3046\u306a P \u3068, \u305d\u306e\u3068\u304d\u306e $\\text{PQ}^2 +\\text{PR}^2$ \u3092\u6c42\u3081\u3088. <\/p>\r\n<hr>\r\n<!--more-->\r\n<h2>\u3010 \u89e3 \u7b54 \u3011<\/h2>\r\n<p>\u6761\u4ef6\u3088\u308a, \u5b9f\u6570 $p , q , r$ \u3092\u7528\u3044\u3066\r\n$$\\begin{align}\r\n\\overrightarrow{\\text{OP}} &amp; = \\overrightarrow{\\text{OA}} +p \\overrightarrow{u} = \\left( \\begin{array}{c} 2p+1 \\\\ p \\\\ -p-2 \\end{array} \\right) , \\\\\r\n\\overrightarrow{\\text{OQ}} &amp; = \\overrightarrow{\\text{OB}} +q \\overrightarrow{v} = \\left( \\begin{array}{c} q+1 \\\\ -q+2 \\\\ q-3 \\end{array} \\right) , \\\\\r\n\\overrightarrow{\\text{OR}} &amp; = \\overrightarrow{\\text{OC}} +r \\overrightarrow{w} = \\left( \\begin{array}{c} r+1 \\\\ 2r-1 \\\\ r \\end{array} \\right)\r\n\\end{align}$$\r\n\u3068\u8868\u305b\u308b\u306e\u3067\r\n$$\r\n\\overrightarrow{\\text{PQ}} = \\left( \\begin{array}{c} -2p+q \\\\ -p-q+2 \\\\ p+q-1 \\end{array} \\right) , \\quad \\overrightarrow{\\text{PR}} = \\left( \\begin{array}{c} -2p+r \\\\ -p+2r-1 \\\\ p+r+2 \\end{array} \\right) \\quad ... \\maru{1}\r\n$$\r\n$\\overrightarrow{\\text{PQ}} \\perp \\overrightarrow{v}$ , $\\overrightarrow{\\text{PR}} \\perp \\overrightarrow{w}$ \u306a\u306e\u3067\r\n$$\\begin{align}\r\n\\overrightarrow{\\text{PQ}} \\cdot \\overrightarrow{v} &amp; = ( -2p+q ) -( -p-q+2 ) +( p+q-1 ) \\\\\r\n&amp; = 3q -3 = 0 \\\\\r\n&amp; \\therefore \\quad q = 1 , \\\\\r\n\\overrightarrow{\\text{PR}} \\cdot \\overrightarrow{w} &amp; = ( -2p+r ) +2( -p+2r-1 ) +( p+r+2 ) \\\\\r\n&amp; = -3p +6r = 0 \\\\\r\n&amp; \\therefore \\quad p = 2r\r\n\\end{align}$$\r\n$\\maru{1}$ \u306b\u4ee3\u5165\u3059\u308b\u3068\r\n$$\r\n\\overrightarrow{\\text{PQ}} = \\left( \\begin{array}{c} -4r+1 \\\\ -2r+1 \\\\ 2r \\end{array} \\right) , \\quad \\overrightarrow{\\text{PR}} = \\left( \\begin{array}{c} -3r \\\\ -1 \\\\ 3r+2 \\end{array} \\right)\r\n$$\r\n\u3057\u305f\u304c\u3063\u3066\r\n$$\\begin{align}\r\n\\text{PQ}^2 +\\text{PR}^2 &amp; = (-4r+1)^2 +(-2r+1)^2 +(2r)^2 \\\\\r\n&amp; \\qquad +(-3r)^2 +(-1)^2 +(3r+2)^2 \\\\\r\n&amp; = 42 r^2 +7\r\n\\end{align}$$\r\n\u3053\u308c\u306f, $r = 0$ \u306e\u3068\u304d\u306b\u6700\u5c0f\u3068\u306a\u308b.<br \/>\r\n\u3088\u3063\u3066, $\\text{PQ}^2 +\\text{PR}^2$ \u306f $\\underline{\\text{P} \\ ( 1, 0, -2 )}$ \u306e\u3068\u304d, \u6700\u5c0f\u5024 $\\underline{7}$ \u3092\u3068\u308b. <\/p>\r\n","protected":false},"excerpt":{"rendered":"\u5ea7\u6a19\u7a7a\u9593\u306b\u304a\u3051\u308b\u6b21\u306e $3$ \u3064\u306e\u76f4\u7dda $l , m , n$ \u3092\u8003\u3048\u308b\uff1a $l$ \u306f\u70b9A $( 1 , 0 , -2 )$ \u3092\u901a\u308a, \u30d9\u30af\u30c8\u30eb $\\overrightarrow{u} = ( 2 , 1 , -1 )$ &hellip; <a href=\"https:\/\/www.roundown.net\/nyushi\/kyr201401\/\">\u7d9a\u304d\u3092\u8aad\u3080 <span class=\"meta-nav\">&rarr;<\/span><\/a>","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"inline_featured_image":false,"footnotes":""},"categories":[114],"tags":[140,112],"class_list":["post-1110","post","type-post","status-publish","format-standard","hentry","category-kyoto_r_2014","tag-kyoto_r","tag-112"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1110","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/comments?post=1110"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1110\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=1110"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=1110"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=1110"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}