{"id":1162,"date":"2015-07-11T22:58:46","date_gmt":"2015-07-11T13:58:46","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=1162"},"modified":"2021-09-23T09:00:57","modified_gmt":"2021-09-23T00:00:57","slug":"thr201402","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/thr201402\/","title":{"rendered":"\u6771\u5317\u5927\u7406\u7cfb2014\uff1a\u7b2c2\u554f"},"content":{"rendered":"
\n

\u4e0b\u56f3\u306e\u3088\u3046\u306a\u5e73\u884c\u516d\u9762\u4f53 OABC-DEFG \u304c \\(xyz\\) \u7a7a\u9593\u5185\u306b\u3042\u308a, O \\(( 0 , 0 , 0 )\\) , A \\(( 2 , 0 , 0 )\\) , C \\(( 0 , 3 , 0 )\\) , D \\(( -1 , 0 , \\sqrt{6} )\\) \u3068\u3059\u308b. \u8fba AB \u306e\u4e2d\u70b9\u3092 M \u3068\u3057, \u8fba DG \u4e0a\u306e\u70b9 N \u3092 \\(\\text{MN} = 4\\) \u304b\u3064 \\(\\text{DN} \\lt \\text{GN}\\) \u3092\u6e80\u305f\u3059\u3088\u3046\u306b\u5b9a\u3081\u308b.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000N \u306e\u5ea7\u6a19\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\\(3\\) \u70b9 E, M, N \u3092\u901a\u308b\u5e73\u9762\u3068 \\(y\\) \u8ef8\u3068\u306e\u4ea4\u70b9 P \u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n

  3. (3)<\/strong>\u3000\\(3\\) \u70b9 E, M, N \u3092\u901a\u308b\u5e73\u9762\u306b\u3088\u308b\u5e73\u884c\u516d\u9762\u4f53 OABC-DEFG \u306e\u5207\u308a\u53e3\u306e\u9762\u7a4d\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n<\/ol>\r\n\"thr20140201\"\r\n

    \r\n\r\n

    \u3010 \u89e3 \u7b54 \u3011<\/h2>\r\n\"thr20140202\"\r\n

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

    \\[\r\n\\text{AD} = \\sqrt{3^2 +6} = \\sqrt{15} \\ .\r\n\\]\r\nM \u304b\u3089 DG \u306b\u4e0b\u308d\u3057\u305f\u5782\u7dda\u306e\u8db3\u3092 H \u3068\u304a\u3051\u3070, H \\(\\left( 0 , \\dfrac{3}{2} , \\sqrt{6} \\right)\\) \u3067\u3042\u308a\r\n\\[\r\n\\text{MH} = \\text{AD} = \\sqrt{15} \\ .\r\n\\]\r\n\\(\\text{HN} = t\\) \u3068\u304a\u3051\u3070, \u25b3MHN \u306f\u76f4\u89d2\u4e09\u89d2\u5f62\u306a\u306e\u3067\r\n\\[\\begin{align}\r\n15 +t^2 & = 4^2 \\\\\r\n\\text{\u2234} \\quad t & = 1 \\ .\r\n\\end{align}\\]\r\n\\(\\text{DN} \\lt \\text{GN}\\) \u306a\u306e\u3067\r\n\\[\r\n\\text{N} \\ \\underline{\\left( -1 , \\dfrac{1}{2} , \\sqrt{6} \\right)} \\ .\r\n\\]\r\n

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

    \u56db\u89d2\u5f62 EMPN \u306f\u5e73\u884c\u56db\u8fba\u5f62\u306b\u306a\u308b\u306e\u3067\r\n\\[\r\n\\overrightarrow{\\text{MP}} = \\overrightarrow{\\text{EN}} = \\left( -2 , \\dfrac{1}{2} , 0 \\right) \\ .\r\n\\]\r\n\u3088\u3063\u3066\r\n\\[\r\n\\text{P} \\ \\underline{\\left( 0 , \\dfrac{3}{2} , 0 \\right)} \\ .\r\n\\]\r\n

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

    \\[\\begin{align}\r\n\\overrightarrow{\\text{PM}} & = \\left( 2 , -\\dfrac{1}{2} , 0 \\right) , \\\\\r\n\\overrightarrow{\\text{PN}} & = \\left( -1 , -\\dfrac{3}{2} , \\sqrt{6} \\right) \\ .\r\n\\end{align}\\]\r\n\u306a\u306e\u3067\r\n\\[\\begin{align}\r\n\\left| \\overrightarrow{\\text{PM}} \\right|^2 & = 2^2 +\\left( -\\dfrac{1}{2} \\right)^2 +0 = \\dfrac{17}{4} , \\\\\r\n\\left| \\overrightarrow{\\text{PN}} \\right|^2 & = (-1)^2 +\\left( -\\dfrac{3}{2} \\right)^2 +6 = \\dfrac{37}{4} , \\\\\r\n\\overrightarrow{\\text{PM}} \\cdot \\overrightarrow{\\text{PN}} & = 2 (-1) -\\dfrac{1}{2} \\left( -\\dfrac{3}{2} \\right) +0 \\cdot \\sqrt{6} = -\\dfrac{5}{4} \\ .\r\n\\end{align}\\]\r\n\u3088\u3063\u3066, \u6c42\u3081\u308b\u9762\u7a4d \\(S\\) \u306f\r\n\\[\\begin{align}\r\nS & = \\sqrt{\\left| \\overrightarrow{\\text{PM}} \\right|^2 \\left| \\overrightarrow{\\text{PN}} \\right|^2 -\\left( \\overrightarrow{\\text{PM}} \\cdot \\overrightarrow{\\text{PN}} \\right)^2} \\\\\r\n& = \\sqrt{\\dfrac{17}{4} \\cdot \\dfrac{37}{4} -\\left( -\\dfrac{5}{4} \\right)^2} \\\\\r\n& = \\underline{\\dfrac{\\sqrt{151}}{2}} \\ .\r\n\\end{align}\\]\r\n","protected":false},"excerpt":{"rendered":"\u4e0b\u56f3\u306e\u3088\u3046\u306a\u5e73\u884c\u516d\u9762\u4f53 OABC-DEFG \u304c \\(xyz\\) \u7a7a\u9593\u5185\u306b\u3042\u308a, O \\(( 0 , 0 , 0 )\\) , A \\(( 2 , 0 , 0 )\\) , C \\(( 0 , 3 , 0 )\\) , D \\( … \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":[118],"tags":[148,112],"class_list":["post-1162","post","type-post","status-publish","format-standard","hentry","category-tohoku_r_2014","tag-tohoku_r","tag-112"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1162","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=1162"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1162\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=1162"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=1162"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=1162"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}