{"id":67,"date":"2011-11-26T20:48:25","date_gmt":"2011-11-26T11:48:25","guid":{"rendered":"http:\/\/roundown.main.jp\/nyushi\/?p=67"},"modified":"2021-10-23T04:18:05","modified_gmt":"2021-10-22T19:18:05","slug":"wsr201105","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/wsr201105\/","title":{"rendered":"\u65e9\u7a32\u7530\u7406\u5de52011\uff1a\u7b2c5\u554f"},"content":{"rendered":"
\n

\u56db\u9762\u4f53 OABC \u306b\u304a\u3044\u3066 \\(\\text{OA} = \\text{BC} = 2\\) , \\(\\text{OB} = 3\\) , \\(\\text{OC} = \\text{AB} = 4\\) , \\(\\text{AC} = 2 \\sqrt{6}\\) \u3067\u3042\u308b.\r\n\u307e\u305f, \\(\\overrightarrow{a} = \\overrightarrow{\\text{OA}}\\) , \\(\\overrightarrow{b} = \\overrightarrow{\\text{OB}}\\) , \\(\\overrightarrow{c} = \\overrightarrow{\\text{OC}}\\) \u3068\u3059\u308b. \u4ee5\u4e0b\u306e\u554f\u306b\u7b54\u3048\u3088.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\u5185\u7a4d \\(\\overrightarrow{a} \\cdot \\overrightarrow{b}\\) , \\(\\overrightarrow{a} \\cdot \\overrightarrow{c}\\) , \\(\\overrightarrow{b} \\cdot \\overrightarrow{c}\\) \u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\\(\\triangle \\text{OAB}\\) \u3092\u542b\u3080\u5e73\u9762\u3092 \\(H\\) \u3068\u3059\u308b. \\(H\\) \u4e0a\u306e\u70b9 P \u3067\u76f4\u7dda PC \u3068 \\(H\\) \u304c\u76f4\u4ea4\u3059\u308b\u3082\u306e\u3092\u3068\u308b. \u3053\u306e\u3068\u304d, \\(\\overrightarrow{\\text{OP}} = x \\overrightarrow{a} +y \\overrightarrow{b}\\) \u3068\u306a\u308b \\(x , y\\) \u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n

  3. (3)<\/strong>\u3000\u5e73\u9762 \\(H\\) \u3092\u76f4\u7dda OA , AB , BO \u3067\u4e0b\u56f3\u306e\u3088\u3046\u306b \\(7\\) \u3064\u306e\u9818\u57df\u30a2, \u30a4, \u30a6, \u30a8, \u30aa, \u30ab, \u30ad\u306b\u308f\u3051\u308b. \u70b9 P \u306f\u3069\u306e\u9818\u57df\u306b\u5165\u308b\u304b\u7b54\u3048\u3088.<\/p><\/li>\r\n\"waseda_2011_05_01\"\r\n

  4. (4)<\/strong>\u3000\u8fba AB \u3067 \u25b3ABC \u3068 \u25b3OAB \u306e\u306a\u3059\u89d2\u306f\u92ed\u89d2\u306b\u306a\u308b\u304b, \u76f4\u89d2\u306b\u306a\u308b\u304b, \u305d\u308c\u3068\u3082\u920d\u89d2\u306b\u306a\u308b\u304b\u3092\u5224\u5b9a\u305b\u3088. \u305f\u3060\u3057, \\(1\\) \u8fba\u3092\u5171\u6709\u3059\u308b \\(2\\) \u3064\u306e\u4e09\u89d2\u5f62\u306e\u306a\u3059\u89d2\u3068\u306f, \u5171\u6709\u3059\u308b\u8fba\u306b\u76f4\u4ea4\u3059\u308b\u5e73\u9762\u3067\u306e \\(2\\) \u3064\u306e\u4e09\u89d2\u5f62\u306e\u5207\u308a\u53e3\u306e\u306a\u3059\u89d2\u306e\u3053\u3068\u3067\u3042\u308b.<\/li>\r\n<\/ol>\r\n
    \r\n\r\n

    \u3010 \u89e3 \u7b54 \u3011<\/h2>\r\n

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

    \\(\\left| \\overrightarrow{a} \\right| = 2\\) , \\(\\left| \\overrightarrow{b} \\right| = 3\\) , \\(\\left| \\overrightarrow{c} \\right| = 4\\) \u3092\u7528\u3044\u3066\r\n\\[\\begin{gather}\r\n\\left| \\overrightarrow{a} -\\overrightarrow{b} \\right|^2 = 4 +9 - 2\\overrightarrow{a} \\cdot \\overrightarrow{b} = 16 \\\\\r\n\\text{\u2234} \\quad \\overrightarrow{a} \\cdot \\overrightarrow{b} = \\underline{-\\dfrac{3}{2}} , \\\\\r\n\\left| \\overrightarrow{c} -\\overrightarrow{a} \\right|^2 = 16 +4 - 2\\overrightarrow{a} \\cdot \\overrightarrow{c} = 24 \\\\\r\n\\text{\u2234} \\quad \\overrightarrow{a} \\cdot \\overrightarrow{c} = \\underline{-2} , \\\\\r\n\\left| \\overrightarrow{b} -\\overrightarrow{c} \\right|^2 = 9 +16 - 2\\overrightarrow{a} \\cdot \\overrightarrow{b} = 4 \\\\\r\n\\text{\u2234} \\quad \\overrightarrow{b} \\cdot \\overrightarrow{c} = \\underline{\\dfrac{21}{2}}\r\n\\end{gather}\\]\r\n

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

    PC \u3068\u5e73\u9762 \\(H\\) \u306f\u5782\u76f4\u306a\u306e\u3067\r\n\\[\r\n\\overrightarrow{\\text{CP}} \\perp \\overrightarrow{\\text{OA}} , \\ \\overrightarrow{\\text{CP}} \\perp \\overrightarrow{\\text{OB}}\r\n\\]\r\n\u3057\u305f\u304c\u3063\u3066,\r\n\\[\\begin{align}\r\n\\left( x \\overrightarrow{a} +y \\overrightarrow{b} -\\overrightarrow{c} \\right) \\cdot \\overrightarrow{a} & = 4x -\\dfrac{3y}{2} +2 = 0 \\\\\r\n\\text{\u2234} \\quad 8x-3y & = -4 \\quad ... [1] , \\\\\r\n\\left( x \\overrightarrow{a} +y \\overrightarrow{b} -\\overrightarrow{c} \\right) \\cdot \\overrightarrow{b} & = -\\dfrac{3x}{2} +9y -\\dfrac{21}{2} = 0 \\\\\r\n\\text{\u2234} \\quad x-6y & = 7 \\quad ... [2]\r\n\\end{align}\\]\r\n[1] [2] \u3092\u89e3\u3051\u3070\r\n\\[\r\nx = \\underline{-\\dfrac{1}{15}} , \\ y = \\underline{\\dfrac{52}{45}}\r\n\\]\r\n

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

    (2)<\/strong> \u306e\u7d50\u679c\u3088\u308a\r\n\\[\r\n\\overrightarrow{\\text{OH}} =\\dfrac{-3 \\overrightarrow{a} +52 \\overrightarrow{b}}{45} = \\dfrac{49}{45} \\cdot \\dfrac{-3 \\overrightarrow{a} +52 \\overrightarrow{b}}{49}\r\n\\]\r\n\u306a\u306e\u3067, \u7dda\u5206 AB \u3092 \\(52 : 3\\) \u306b\u5916\u5206\u3059\u308b\u70b9\u3092 Q \u3068\u3059\u308b\u3068\u304d, \u70b9 P \u306f\u7dda\u5206 OQ \u3092 \\(49 : 4\\) \u306b\u5916\u5206\u3059\u308b\u70b9\u3067\u3042\u308b.
    \r\n\u3086\u3048\u306b, \u70b9 P \u3092\u542b\u3080\u9818\u57df\u306f\r\n\\[\r\n\\underline{\\text{\u30a6}}\r\n\\]\r\n

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

    (3)<\/strong> \u306e\u7d50\u679c\u3088\u308a, \u70b9 P \u304c\u76f4\u7dda AB \u306b\u3064\u3044\u3066, \u70b9 O \u3068\u53cd\u5bfe\u5074\u306b\u3042\u308b\u306e\u3067, \u25b3ABC \u3068 \u25b3OAB \u306e\u306a\u3059\u89d2\u306f\r\n\\[\r\n\\underline{\\text{\u920d\u89d2}}\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"\u56db\u9762\u4f53 OABC \u306b\u304a\u3044\u3066 \\(\\text{OA} = \\text{BC} = 2\\) , \\(\\text{OB} = 3\\) , \\(\\text{OC} = \\text{AB} = 4\\) , \\(\\text{AC} … \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":[38],"tags":[147,13],"class_list":["post-67","post","type-post","status-publish","format-standard","hentry","category-waseda_r_2011","tag-waseda_r","tag-13"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/67","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=67"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/67\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=67"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=67"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=67"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}