{"id":2024,"date":"2021-12-11T10:01:31","date_gmt":"2021-12-11T01:01:31","guid":{"rendered":"https:\/\/www.roundown.net\/nyushi\/?p=2024"},"modified":"2021-12-11T10:01:31","modified_gmt":"2021-12-11T01:01:31","slug":"tbr202103","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/tbr202103\/","title":{"rendered":"\u7b51\u6ce2\u5927\u7406\u7cfb2021\uff1a\u7b2c3\u554f"},"content":{"rendered":"
\n

O \u3092\u539f\u70b9\u3068\u3059\u308b\u5ea7\u6a19\u7a7a\u9593\u306b\u304a\u3044\u3066,\r\n\\(3\\) \u70b9 A \\(( -2 , 0 , 0 )\\) , B \\(( 0 , 1 , 0 )\\) , C \\(( 0 , 0 , 1 )\\) \u3092\u901a\u308b\u5e73\u9762\u3092 \\(\\alpha\\) \u3068\u3059\u308b.\r\n\\(2\\) \u70b9 P \\(( 0 , 5 , 5 )\\) , Q \\(( 1 , 1 , 1 )\\) \u3092\u3068\u308b.\r\n\u70b9 P \u3092\u901a\u308a \\(\\overrightarrow{\\text{OQ}}\\) \u306b\u5e73\u884c\u306a\u76f4\u7dda\u3092 \\(\\ell\\) \u3068\u3059\u308b.\r\n\u76f4\u7dda \\(\\ell\\) \u4e0a\u306e\u70b9 R \u304b\u3089\u5e73\u9762 \\(\\alpha\\) \u306b\u4e0b\u3057\u305f\u5782\u7dda\u3068 \\(\\alpha\\) \u306e\u4ea4\u70b9\u3092 S \u3068\u3059\u308b.\r\n\\(\\overrightarrow{\\text{OR}} = \\overrightarrow{\\text{OP}} +k \\overrightarrow{\\text{OQ}}\\) \uff08\u305f\u3060\u3057 \\(k\\) \u306f\u5b9f\u6570\uff09\u3068\u304a\u304f\u3068\u304d, \u4ee5\u4e0b\u306e\u554f\u3044\u306b\u7b54\u3048\u3088.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\\(k\\) \u3092\u7528\u3044\u3066, \\(\\overrightarrow{\\text{AS}}\\) \u3092\u6210\u5206\u3067\u8868\u305b.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\u70b9 S \u304c \\(\\triangle \\text{ABC}\\) \u306e\u5185\u90e8\u307e\u305f\u306f\u5468\u306b\u3042\u308b\u3088\u3046\u306a \\(k\\) \u306e\u5024\u306e\u7bc4\u56f2\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n<\/ol>\r\n

    \r\n\r\n

    \u3010 \u89e3 \u7b54 \u3011<\/h4>\r\n

    (1)<\/strong><\/p>\r\n

    \\(\\alpha\\) \u306e\u5f0f\u306f\r\n\\[\\begin{align}\r\n-\\dfrac{x}{2} +y +z & = 1 \\quad ... [1] \\\\\r\n\\text{\u2234} \\quad z & = \\dfrac{x}{2} -y +1 \\quad ... [2]\r\n\\end{align}\\]\r\n[1]\u3088\u308a, \\(\\alpha\\) \u306b\u5782\u76f4\u306a\u30d9\u30af\u30c8\u30eb\u306e \\(1\\) \u3064\u306f \\(\\left( \\begin{array}{c} -\\dfrac{1}{2} \\\\ 1 \\\\ 1 \\end{array} \\right)\\) .\r\n\\[\r\n\\overrightarrow{\\text{OR}} = \\overrightarrow{\\text{OP}} +k \\overrightarrow{\\text{OQ}} = \\left( \\begin{array}{c} k \\\\ k+5 \\\\ k+5 \\end{array} \\right)\r\n\\]\r\n\u306a\u306e\u3067, [2] \u3082\u7528\u3044\u3066\r\n\\[\r\n\\overrightarrow{\\text{RS}} = \\overrightarrow{\\text{OS}} -\\overrightarrow{\\text{OR}} = \\left( \\begin{array}{c} x-k \\\\ y -k -5 \\\\ \\dfrac{x}{2} -y -k-4 \\end{array} \\right)\r\n\\]\r\n\u307e\u305f, \u5b9f\u6570 \\(m\\) \u3092\u7528\u3044\u3066\r\n\\[\r\n\\overrightarrow{\\text{RS}} = m \\left( \\begin{array}{c} -\\dfrac{1}{2} \\\\ 1 \\\\ 1 \\end{array} \\right)\r\n\\]\r\n\u3086\u3048\u306b, \u6210\u5206\u3092\u6bd4\u8f03\u3057\u3066\r\n\\[\r\n\\left\\{ \\begin{array}{ll} x-k = -\\dfrac{m}{2} & ... [3] \\\\ y -k -5 = m & ... [4] \\\\ \\dfrac{x}{2} -y -k -4 = m & ... [5] \\end{array} \\right.\r\n\\]\r\n[4] [5] \u3088\u308a\r\n\\[\\begin{align}\r\ny -k -5 & = \\dfrac{x}{2} -y -k -4 \\\\\r\n\\text{\u2234} \\quad x & = 4y -2 \\quad ... [6]\r\n\\end{align}\\]\r\n[3] \u306b\u4ee3\u5165\u3057\u3066\r\n\\[\\begin{align}\r\n-2 ( 4y -k ) & = y -k -5 \\\\\r\n9y & = 3k +9 \\\\\r\n\\text{\u2234} \\quad y & = \\dfrac{k}{3} +1\r\n\\end{align}\\]\r\n[2] [6] \u3088\u308a\r\n\\[\\begin{align}\r\nx & = \\dfrac{4}{3} k +2 \\ , \\\\\r\nz & = \\dfrac{2}{3} k +1 -\\dfrac{k}{3} -1 +1 = \\dfrac{k}{3} +1\r\n\\end{align}\\]\r\n\u3086\u3048\u306b\r\n\\[\r\n\\text{S} \\ \\left( \\dfrac{4}{3} k +2 , \\dfrac{k}{3} +1 , \\dfrac{k}{3} +1 \\right)\r\n\\]\r\n\u3088\u3063\u3066\r\n\\[\r\n\\overrightarrow{\\text{AS}} = \\overrightarrow{\\text{OS}} -\\overrightarrow{\\text{OA}} = \\underline{\\left( \\dfrac{k}{3} +1 \\right) \\left( \\begin{array}{c} 4 \\\\ 1 \\\\ 1 \\end{array} \\right)}\r\n\\]\r\n

    (2)<\/strong><\/p>\r\n

    BC \u306e\u4e2d\u70b9\u3092 M \u3068\u304a\u304f\u3068, \\(\\overrightarrow{\\text{AB}} = \\left( \\begin{array}{c} 2 \\\\ 1 \\\\ 0 \\end{array} \\right)\\) , \\(\\overrightarrow{\\text{AC}} = \\left( \\begin{array}{c} 2 \\\\ 0 \\\\ 1 \\end{array} \\right)\\) \u306a\u306e\u3067\r\n\\[\\begin{align}\r\n\\overrightarrow{\\text{AS}} = \\left( \\dfrac{k}{3} +1 \\right) \\left( \\overrightarrow{\\text{AB}} +\\overrightarrow{\\text{AC}} \\right) = 2 \\left( \\dfrac{k}{3} +1 \\right) \\overrightarrow{\\text{AM}}\r\n\\end{align}\\]\r\n\u3057\u305f\u304c\u3063\u3066, \u70b9 S \u304c\u6761\u4ef6\u3092\u307f\u305f\u3059\u306e\u306f, \u7dda\u5206 AM \u4e0a\u306b\u3042\u308b\u3068\u304d\u3067, \u6c42\u3081\u308b \\(k\\) \u5024\u306e\u7bc4\u56f2\u306f\r\n\\[\\begin{gather}\r\n0 \\leqq 2 \\left( \\dfrac{k}{3} +1 \\right) \\leqq 1 \\\\\r\n-1 \\leqq \\dfrac{k}{3} \\leqq -\\dfrac{1}{2} \\\\\r\n\\text{\u2234} \\quad \\underline{-3 \\leqq k \\leqq -\\dfrac{3}{2}}\r\n\\end{gather}\\]\r\n","protected":false},"excerpt":{"rendered":"O \u3092\u539f\u70b9\u3068\u3059\u308b\u5ea7\u6a19\u7a7a\u9593\u306b\u304a\u3044\u3066, \\(3\\) \u70b9 A \\(( -2 , 0 , 0 )\\) , B \\(( 0 , 1 , 0 )\\) , C \\(( 0 , 0 , 1 )\\) \u3092\u901a\u308b\u5e73\u9762\u3092 \\(\\alpha\\) \u3068 … \u7d9a\u304d\u3092\u8aad\u3080 →<\/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":[178],"tags":[144,165],"class_list":["post-2024","post","type-post","status-publish","format-standard","hentry","category-tsukuba_r_2021","tag-tsukuba_r","tag-165"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/2024","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=2024"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/2024\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=2024"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=2024"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=2024"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}