{"id":1364,"date":"2016-12-29T01:50:00","date_gmt":"2016-12-28T16:50:00","guid":{"rendered":"http:\/\/www.roundown.net\/nyushi\/?p=1364"},"modified":"2021-11-03T20:04:34","modified_gmt":"2021-11-03T11:04:34","slug":"htb201504","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/htb201504\/","title":{"rendered":"\u4e00\u6a4b\u59272015\uff1a\u7b2c4\u554f"},"content":{"rendered":"
\n

\\(xyz\\) \u7a7a\u9593\u306b\u304a\u3044\u3066, \u539f\u70b9\u3092\u4e2d\u5fc3\u3068\u3059\u308b \\(xy\\) \u5e73\u9762\u4e0a\u306e\u534a\u5f84 \\(1\\) \u306e\u5186\u5468\u4e0a\u3092\u70b9 P \u304c\u52d5\u304d, \u70b9 \\(( 0 , 0 , \\sqrt{3} )\\) \u3092\u4e2d\u5fc3\u3068\u3059\u308b \\(xz\\) \u5e73\u9762\u4e0a\u306e\u534a\u5f84 \\(1\\) \u306e\u5186\u5468\u4e0a\u3092\u70b9 Q \u304c\u52d5\u304f.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\u7dda\u5206 PQ \u306e\u9577\u3055\u306e\u6700\u5c0f\u5024\u3068, \u305d\u306e\u3068\u304d\u306e\u70b9 P , Q \u306e\u5ea7\u6a19\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\u7dda\u5206 PQ \u306e\u9577\u3055\u306e\u6700\u5927\u5024\u3068, \u305d\u306e\u3068\u304d\u306e\u70b9 P , Q \u306e\u5ea7\u6a19\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n<\/ol>\r\n

    \r\n\r\n

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

    \u6761\u4ef6\u3088\u308a, P , Q \u306e\u5ea7\u6a19\u306f \\( 0 \\leqq \\alpha , \\beta \\lt 2 \\pi\\) \u3092\u7528\u3044\u3066\r\n\\[\r\n\\text{P} \\ \\left( \\cos \\alpha , \\sin \\alpha , 0 \\right) , \\quad \\text{Q} \\ \\left( \\cos \\beta , 0 , \\sqrt{3} +\\sin \\beta \\right)\r\n\\]\r\n\u3057\u305f\u304c\u3063\u3066\r\n\\[\\begin{align}\r\n\\left| \\overrightarrow{\\text{PQ}} \\right|^2 & = ( \\cos \\alpha -\\cos \\beta )^2 +\\sin^2 \\alpha +( \\sqrt{3} +\\sin \\beta )^2 \\\\\r\n& = -2 \\cos \\alpha \\cos \\beta +2 \\sqrt{3} \\sin \\beta +5\r\n\\end{align}\\]\r\n\\(t = \\cos \\alpha\\) \u3068\u304a\u3051\u3070, \\(-1 \\leqq t \\leqq 1\\) .
    \r\n\\(\\beta\\) \u3092\u5b9a\u6570\u3068\u3059\u308c\u3070, \\(\\left| \\overrightarrow{\\text{PQ}} \\right|^2\\) \u306f \\(t\\) \u306e \\(1\\) \u6b21\u95a2\u6570\u306a\u306e\u3067, \u6700\u5927\u6700\u5c0f\u306e\u5019\u88dc\u306f\r\n\\[\\begin{align}\r\n& \\pm 2 \\cos \\beta +2 \\sqrt{3} \\sin \\beta +5 \\\\\r\n& \\qquad = 4 \\left( \\sin \\beta \\cos \\dfrac{\\pi}{6} \\pm \\cos \\beta \\sin \\dfrac{\\pi}{6} \\right) +5\\\\\r\n& \\qquad = 4 \\sin \\left( \\beta \\pm \\dfrac{\\pi}{6} \\right) +5\r\n\\end{align}\\]\r\n\u3053\u308c\u304c\u6700\u5927\u3068\u306a\u308b\u306e\u306f, \\(\\beta \\pm \\dfrac{\\pi}{6} = \\dfrac{\\pi}{2}\\) \u306e\u3068\u304d\u3067\r\n\\[\r\n( \\alpha , \\beta ) = \\left( \\pi , \\dfrac{\\pi}{3} \\right) , \\ \\left( 0 , \\dfrac{2 \\pi}{3} \\right)\r\n\\]\r\n\u307e\u305f, \u6700\u5c0f\u3068\u306a\u308b\u306e\u306f, \\(\\beta \\pm \\dfrac{\\pi}{6} = \\dfrac{3 \\pi}{2}\\) \u306e\u3068\u304d\u3067\r\n\\[\r\n( \\alpha , \\beta ) = \\left( \\pi , \\dfrac{4 \\pi}{3} \\right) , \\ \\left( 0 , \\dfrac{5 \\pi}{3} \\right)\r\n\\]\r\n

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

    \\[\r\n\\underline{\\text{P} \\ ( \\pm 1 , 0 , 0 ) ,\\ \\text{Q} \\ \\left( \\pm \\dfrac{1}{2} , 0 , \\dfrac{\\sqrt{3}}{2} \\right) \\quad \\text{\uff08\u8907\u53f7\u540c\u9806\uff09} \\ }\r\n\\]\r\n\u306e\u3068\u304d, \u6700\u5c0f\u5024\r\n\\[\r\n\\underline{1}\r\n\\]\r\n

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

    \\[\r\n\\underline{\\text{P} \\ ( \\pm 1 , 0 , 0 ) ,\\ \\text{Q} \\ \\left( \\mp \\dfrac{1}{2} , 0 , \\dfrac{3 \\sqrt{3}}{2} \\right) \\quad \\text{\uff08\u8907\u53f7\u540c\u9806\uff09} \\ }\r\n\\]\r\n\u306e\u3068\u304d, \u6700\u5927\u5024\r\n\\[\r\n\\underline{3}\r\n\\]\r\n","protected":false},"excerpt":{"rendered":"\\(xyz\\) \u7a7a\u9593\u306b\u304a\u3044\u3066, \u539f\u70b9\u3092\u4e2d\u5fc3\u3068\u3059\u308b \\(xy\\) \u5e73\u9762\u4e0a\u306e\u534a\u5f84 \\(1\\) \u306e\u5186\u5468\u4e0a\u3092\u70b9 P \u304c\u52d5\u304d, \u70b9 \\(( 0 , 0 , \\sqrt{3} )\\) \u3092\u4e2d\u5fc3\u3068\u3059\u308b \\(xz\\) \u5e73\u9762\u4e0a\u306e\u534a\u5f84 \\(1 … \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":[136],"tags":[146,137],"class_list":["post-1364","post","type-post","status-publish","format-standard","hentry","category-hitotsubashi_2015","tag-hitotsubashi","tag-137"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1364","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=1364"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1364\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=1364"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=1364"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=1364"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}