{"id":655,"date":"2013-02-24T13:45:32","date_gmt":"2013-02-24T04:45:32","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=655"},"modified":"2021-09-10T19:08:10","modified_gmt":"2021-09-10T10:08:10","slug":"osr200703","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/osr200703\/","title":{"rendered":"\u962a\u5927\u7406\u7cfb2007\uff1a\u7b2c3\u554f"},"content":{"rendered":"
\n

\\(xy\\) \u5e73\u9762\u306b\u304a\u3044\u3066, \u539f\u70b9 O \u3092\u901a\u308b\u534a\u5f84 \\(r \\ ( r \\gt 0 )\\) \u306e\u5186\u3092 \\(C\\) \u3068\u3057, \u305d\u306e\u4e2d\u5fc3\u3092 A \u3068\u3059\u308b.\r\nO \u3092\u9664\u304f \\(C\\) \u4e0a\u306e\u70b9 P \u306b\u5bfe\u3057, \u6b21\u306e \\(2\\) \u3064\u306e\u6761\u4ef6 (a) , (b) \u3067\u5b9a\u307e\u308b\u70b9 Q \u3092\u8003\u3048\u308b.<\/p>\r\n

    \r\n

  1. (a)\u3000\\(\\overrightarrow{\\text{OP}}\\) \u3068 \\(\\overrightarrow{\\text{OQ}}\\) \u306e\u5411\u304d\u304c\u540c\u3058.<\/p><\/li>\r\n

  2. (b)\u3000\\(\\left| \\overrightarrow{\\text{OP}} \\right| \\left| \\overrightarrow{\\text{OQ}} \\right| = 1\\)<\/p><\/li>\r\n<\/ol>\r\n

    \u4ee5\u4e0b\u306e\u554f\u3044\u306b\u7b54\u3048\u3088.<\/p>\r\n

      \r\n

    1. (1)<\/strong>\u3000\u70b9 P \u304c O \u3092\u9664\u304f \\(C\\) \u4e0a\u3092\u52d5\u304f\u3068\u304d, \u70b9 Q \u306f \\(\\overrightarrow{\\text{OA}}\\) \u306b\u76f4\u4ea4\u3059\u308b\u76f4\u7dda\u4e0a\u3092\u52d5\u304f\u3053\u3068\u3092\u793a\u305b.<\/p><\/li>\r\n

    2. (2)<\/strong>\u3000(1)<\/strong> \u306e\u76f4\u7dda\u3092 \\(l\\) \u3068\u3059\u308b. \\(l\\) \u304c \\(C\\) \u3068 \\(2\\) \u70b9\u3067\u4ea4\u308f\u308b\u3068\u304d, \\(r\\) \u306e\u3068\u308a\u3046\u308b\u5024\u306e\u7bc4\u56f2\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n<\/ol>\r\n

      \r\n\r\n

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

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

      \u6761\u4ef6 (a) (b) \u3088\u308a\r\n\\[\\begin{align}\r\n\\overrightarrow{\\text{OQ}} & = \\dfrac{\\overrightarrow{\\text{OP}}}{\\left| \\overrightarrow{\\text{OP}} \\right|^2} \\\\\r\n\\text{\u2234} \\quad \\overrightarrow{\\text{OP}} & = \\left| \\overrightarrow{\\text{OP}} \\right|^2 \\overrightarrow{\\text{OQ}} \\quad ... [1] \\ .\r\n\\end{align}\\]\r\n\u307e\u305f, P \u306f\u5186 \\(C\\) \u4e0a\u306e\u70b9\u306a\u306e\u3067\r\n\\[\r\n\\overrightarrow{\\text{OP}} \\cdot \\left( \\overrightarrow{\\text{OP}} -2 \\overrightarrow{\\text{OA}} \\right) = 0 \\ .\r\n\\]\r\n[1] \u3092\u4ee3\u5165\u3059\u308c\u3070\r\n\\[\\begin{align}\r\n\\left| \\overrightarrow{\\text{OP}} \\right|^2 \\overrightarrow{\\text{OQ}} \\cdot \\left( \\left| \\overrightarrow{\\text{OP}} \\right|^2 \\overrightarrow{\\text{OQ}}-2 \\overrightarrow{\\text{OA}} \\right) & = 0 \\\\\r\n2 \\overrightarrow{\\text{OQ}} \\cdot \\overrightarrow{\\text{OA}} & = \\left| \\overrightarrow{\\text{OP}} \\right|^2 \\left| \\overrightarrow{\\text{OQ}} \\right|^2 \\\\\r\n\\text{\u2234} \\quad \\overrightarrow{\\text{OQ}} \\cdot \\overrightarrow{\\text{OA}} & = \\dfrac{1}{2} \\ .\r\n\\end{align}\\]\r\n\u3057\u305f\u304c\u3063\u3066, \\(\\overrightarrow{\\text{OR}} = \\dfrac{1}{2r^2} \\overrightarrow{\\text{OA}}\\) \u3092\u307f\u305f\u3059\u76f4\u7dda OA \u4e0a\u306e\u70b9 R \u3092\u304a\u3051\u3070\r\n\\[\\begin{align}\r\n\\overrightarrow{\\text{OA}} \\cdot \\overrightarrow{\\text{RQ}} = \\dfrac{1}{2} & -\\dfrac{\\left| \\overrightarrow{\\text{OA}} \\right|^2}{2 r^2} = 0 \\\\\r\n\\text{\u2234} \\quad \\text{OA} & \\perp \\text{RQ} \\ .\r\n\\end{align}\\]\r\n\u3088\u3063\u3066, \u70b9 Q \u306f OA \u306b\u5782\u76f4\u306a\u76f4\u7dda\u4e0a\u3092\u52d5\u304f.<\/p>\r\n

      (2)<\/strong>\r\n\\[\r\n\\left| \\overrightarrow{\\text{OR}} \\right| = \\dfrac{1}{2r^2} \\cdot r = \\dfrac{1}{2r} \\ .\r\n\\]\r\n\u306a\u306e\u3067, \u6c42\u3081\u308b\u6761\u4ef6\u306f OR \u306e\u9577\u3055\u3068 \\(C\\) \u306e\u76f4\u5f84\u3092\u6bd4\u8f03\u3057\u3066\r\n\\[\\begin{align}\r\n\\dfrac{1}{2r} & \\lt 2r \\\\\r\nr^2 & \\gt \\dfrac{1}{4} \\\\\r\n\\text{\u2234} \\quad & \\underline{r \\gt \\dfrac{1}{2}} \\quad ( \\ \\text{\u2235} \\ r \\gt 0 ) \\ .\r\n\\end{align}\\]\r\n","protected":false},"excerpt":{"rendered":"\\(xy\\) \u5e73\u9762\u306b\u304a\u3044\u3066, \u539f\u70b9 O \u3092\u901a\u308b\u534a\u5f84 \\(r \\ ( r \\gt 0 )\\) \u306e\u5186\u3092 \\(C\\) \u3068\u3057, \u305d\u306e\u4e2d\u5fc3\u3092 A \u3068\u3059\u308b. O \u3092\u9664\u304f \\(C\\) \u4e0a\u306e\u70b9 P \u306b\u5bfe\u3057, \u6b21\u306e \\(2\\) \u3064\u306e\u6761\u4ef6 … \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":[89],"tags":[142,109],"class_list":["post-655","post","type-post","status-publish","format-standard","hentry","category-osaka_r_2007","tag-osaka_r","tag-109"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/655","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=655"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/655\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=655"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=655"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=655"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}