{"id":195,"date":"2011-12-02T23:08:45","date_gmt":"2011-12-02T14:08:45","guid":{"rendered":"http:\/\/roundown.main.jp\/nyushi\/?p=195"},"modified":"2021-09-10T08:01:51","modified_gmt":"2021-09-09T23:01:51","slug":"osr200904","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/osr200904\/","title":{"rendered":"\u962a\u5927\u7406\u7cfb2009\uff1a\u7b2c4\u554f"},"content":{"rendered":"
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\u5e73\u9762\u4e0a\u306e\u4e09\u89d2\u5f62 OAB \u3092\u8003\u3048, \u8fba AB \u306e\u4e2d\u70b9\u3092 M \u3068\u3059\u308b.\r\n\\[\r\n\\overrightarrow{a} = \\dfrac{\\overrightarrow{\\text{OA}}}{\\left| \\overrightarrow{\\text{OA}} \\right|} , \\quad \\overrightarrow{b} = \\dfrac{\\overrightarrow{\\text{OB}}}{\\left| \\overrightarrow{\\text{OB}} \\right|}\r\n\\]\r\n\u3068\u304a\u304d, \u70b9 P \u3092 \\(\\overrightarrow{a} \\cdot \\overrightarrow{\\text{OP}} = -\\overrightarrow{b} \\cdot \\overrightarrow{\\text{OP}} \\gt 0\\) \u3067\u3042\u308b\u3088\u3046\u306b\u3068\u308b.\r\n\u76f4\u7dda OP \u306b A \u304b\u3089\u4e0b\u308d\u3057\u305f\u5782\u7dda\u3068\u76f4\u7dda OP \u306e\u4ea4\u70b9\u3092 Q \u3068\u3059\u308b.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\\(\\overrightarrow{\\text{MQ}}\\) \u3068 \\(\\overrightarrow{b}\\) \u306f\u5e73\u884c\u3067\u3042\u308b\u3053\u3068\u3092\u793a\u305b.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\\(\\left| \\overrightarrow{\\text{MQ}} \\right| =\\dfrac{1}{2} \\left( \\left| \\overrightarrow{\\text{OA}} \\right| + \\left| \\overrightarrow{\\text{OB}} \\right| \\right)\\) \u3067\u3042\u308b\u3053\u3068\u3092\u793a\u305b.<\/p><\/li>\r\n<\/ol>\r\n

    \r\n\r\n

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

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

    \u6761\u4ef6\u3088\u308a\r\n\\[\r\n\\left| \\overrightarrow{a} \\right| = \\left| \\overrightarrow{b} \\right| = 1 \\quad ... [1]\n\\]\r\n\\(\\text{OA} = \\alpha\\) , \\(\\text{OB} =\\beta\\) \u3068\u304a\u3051\u3070\r\n\\[\r\n\\overrightarrow{\\text{OA}} = \\alpha \\overrightarrow{a} , \\quad \\overrightarrow{\\text{OB}} =\\beta \\overrightarrow{b}\n\\]\r\n\\(\\overrightarrow{\\text{OP}} =\\overrightarrow{p}\\) , \\(\\overrightarrow{\\text{OQ}} =\\overrightarrow{q}\\) \u3068\u304a\u304f.\r\n\u6761\u4ef6\u3088\u308a\r\n\\[\\begin{align}\r\n\\overrightarrow{a} \\cdot \\overrightarrow{p} & = -\\overrightarrow{b} \\cdot \\overrightarrow{p} \\\\\r\n\\left( \\overrightarrow{a} +\\overrightarrow{b} \\right) \\cdot \\overrightarrow{p} & = 0\n\\end{align}\\]\r\n\"\"\r\n[1] \u304b\u3064\u300c \\(\\overrightarrow{a}\\) \u3068 \\(\\overrightarrow{b}\\) \u306f\u5e73\u884c\u3067\u306a\u3044\u300d ... [2] \u306a\u306e\u3067, \\(\\overrightarrow{p}\\) \u306f \\(\\overrightarrow{a} -\\overrightarrow{b}\\) \u3068\u5e73\u884c\u3067\r\n\\[\r\n\\overrightarrow{p} = t \\left( \\overrightarrow{a} -\\overrightarrow{b} \\right) \\quad ( t \\neq 0 )\r\n\\]\r\n\u3068\u304a\u3051\u308b.
    \r\nQ \u306f OP \u4e0a\u306b\u3042\u308b\u306e\u3067, \u540c\u3058\u3088\u3046\u306b\r\n\\[\r\n\\overrightarrow{q} = t \\left( \\overrightarrow{a} -\\overrightarrow{b} \\right)\n\\]\r\n\u3068\u8868\u305b\u308b.
    \r\n\\(\\text{AQ} \\perp \\text{OQ}\\) \u306a\u306e\u3067\r\n\\[\\begin{align}\r\n\\overrightarrow{\\text{AQ}} \\cdot \\overrightarrow{\\text{OQ}} & =0 \\\\\r\n\\left\\{ (t -\\alpha) \\overrightarrow{a} -t \\overrightarrow{b} \\right\\} \\cdot t \\left( \\overrightarrow{a} -\\overrightarrow{b} \\right) & = 0 \\\\\r\n\\text{\u2234} \\quad ( t-\\alpha ) \\left| \\overrightarrow{a} \\right|^2 -\\left( 2t -\\alpha \\right) \\overrightarrow{a} \\cdot\r\n\\overrightarrow{b} +t \\left| \\overrightarrow{b} \\right|^2 & =0 \\\\\r\n( 2t -\\alpha ) \\left( 1 -\\overrightarrow{a} \\cdot \\overrightarrow{b} \\right) & = 0 \\\\\r\n\\text{\u2234} \\quad t = \\dfrac{\\alpha}{2} \\quad & \\left( \\ \\text{\u2235} \\ [1] [2] \\text{\u3088\u308a, } \\overrightarrow{a} \\cdot \\overrightarrow{b} \\neq 1 \\ \\right)\n\\end{align}\\]\r\n\u3057\u305f\u304c\u3063\u3066\r\n\\[\r\n\\overrightarrow{q} = \\dfrac{\\alpha \\overrightarrow{a} -\\alpha \\overrightarrow{b}}{2}\n\\]\r\n\u3086\u3048\u306b\r\n\\[\\begin{align}\r\n\\overrightarrow{\\text{MQ}} & = \\overrightarrow{\\text{OQ}} -\\overrightarrow{\\text{OM}} \\\\\r\n& = \\dfrac{\\alpha \\overrightarrow{a} -\\alpha \\overrightarrow{b}}{2} -\\dfrac{\\alpha \\overrightarrow{a} -\\beta \\overrightarrow{b}}{2} \\\\\r\n& = -\\dfrac{( \\alpha +\\beta ) \\overrightarrow{b}}{2} \\quad ... [3]\n\\end{align}\\]\r\n\u3088\u3063\u3066\r\n\\[\r\n\\underline{\\overrightarrow{\\text{MQ}} \/ \\! \/ \\overrightarrow{b}}\n\\]\r\n","protected":false},"excerpt":{"rendered":"\u5e73\u9762\u4e0a\u306e\u4e09\u89d2\u5f62 OAB \u3092\u8003\u3048, \u8fba AB \u306e\u4e2d\u70b9\u3092 M \u3068\u3059\u308b. \\[ \\overrightarrow{a} = \\dfrac{\\overrightarrow{\\text{OA}}}{\\left| \\overright … \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":[30],"tags":[142,15],"class_list":["post-195","post","type-post","status-publish","format-standard","hentry","category-osaka_r_2009","tag-osaka_r","tag-15"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/195","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=195"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/195\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=195"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=195"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=195"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}