{"id":374,"date":"2012-04-20T01:23:45","date_gmt":"2012-04-19T16:23:45","guid":{"rendered":"http:\/\/roundown.main.jp\/nyushi\/?p=374"},"modified":"2021-09-24T17:43:19","modified_gmt":"2021-09-24T08:43:19","slug":"tok201201","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/tok201201\/","title":{"rendered":"\u6771\u5de5\u59272012\uff1a\u7b2c1\u554f"},"content":{"rendered":"<ol>\r\n<li><p><strong>(1)<\/strong>\u3000\u8fba\u306e\u9577\u3055\u304c \\(1\\) \u3067\u3042\u308b\u6b63\u56db\u9762\u4f53OABC\u306b\u304a\u3044\u3066\u8fbaAB\u306e\u4e2d\u70b9\u3092D, \u8fbaOC\u306e\u4e2d\u70b9\u3092E\u3068\u3059\u308b. \\(2\\) \u3064\u306e\u30d9\u30af\u30c8\u30eb \\(\\overrightarrow{\\text{DE}}\\) \u3068 \\(\\overrightarrow{\\text{AC}}\\) \u3068\u306e\u5185\u7a4d\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n<li><p><strong>(2)<\/strong>\u3000\\(1\\) \u304b\u3089 \\(6\\) \u307e\u3067\u306e\u76ee\u304c\u305d\u308c\u305e\u308c \\(\\dfrac{1}{6}\\) \u306e\u78ba\u7387\u3067\u51fa\u308b\u3055\u3044\u3053\u308d\u3092\u540c\u6642\u306b \\(3\\) \u500b\u6295\u3052\u308b\u3068\u304d, \u76ee\u306e\u7a4d\u304c \\(10\\) \u306e\u500d\u6570\u306b\u306a\u308b\u78ba\u7387\u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n<\/ol>\r\n<hr>\r\n<!--more-->\r\n<h4>\u3010 \u89e3 \u7b54 \u3011<\/h4>\r\n<p><strong>(1)<\/strong><\/p>\r\n<p>\\(\\overrightarrow{a} =\\overrightarrow{\\text{OA}}\\) , \\(\\overrightarrow{b} =\\overrightarrow{\\text{OB}}\\) , \\(\\overrightarrow{c} =\\overrightarrow{\\text{OC}}\\) \u3068\u304a\u304f\u3068\r\n\\[\\begin{align}\r\n\\left| \\overrightarrow{a} \\right| = \\left| \\overrightarrow{b} \\right| = \\left| \\overrightarrow{c} \\right| & = 1 ,\\\\\r\n\\overrightarrow{a} \\cdot \\overrightarrow{b} = \\overrightarrow{b} \\cdot \\overrightarrow{c} = \\overrightarrow{c} \\cdot \\overrightarrow{a} & = 1 \\cdot 1 \\cdot \\cos 60^{\\circ} = \\dfrac{1}{2}\r\n\\end{align}\\]\r\n\u307e\u305f\r\n\\[\r\n\\overrightarrow{\\text{DE}} = \\dfrac{1}{2} \\left( \\overrightarrow{c} -\\overrightarrow{a} -\\overrightarrow{b} \\right) , \\ \\overrightarrow{\\text{AC}} = \\overrightarrow{c} -\\overrightarrow{a}\r\n\\]\r\n\u306a\u306e\u3067\r\n\\[\\begin{align}\r\n\\overrightarrow{\\text{DE}} \\cdot \\overrightarrow{\\text{AC}} & = \\dfrac{1}{2} \\left( 1 -\\dfrac{1}{2} -\\dfrac{1}{2} +1 -\\dfrac{1}{2} +\\dfrac{1}{2} \\right) \\\\\r\n& =\\underline{\\dfrac{1}{2}}\r\n\\end{align}\\]\r\n<p><strong>(2)<\/strong><\/p>\r\n<p>\u76ee\u306e\u7a4d\u304c \\(2\\) \u306e\u500d\u6570\u306b\u306a\u308b\u4e8b\u8c61\u3092 \\(A\\) , \\(5\\) \u306e\u500d\u6570\u306b\u306a\u308b\u4e8b\u8c61\u3092 \\(B\\) \u3068\u3059\u308b\u3068\r\n\\[\\begin{align}\r\n\\text{P} ( \\overline{A} ) & = \\left( \\dfrac{3}{6} \\right)^3 =\\dfrac{1}{8} , \\\\\r\n\\text{P} ( \\overline{B} ) & = \\left( \\dfrac{5}{6} \\right)^3 = \\dfrac{125}{216} , \\\\\r\n\\text{P} ( \\overline{A \\cup B} ) & = \\left( \\dfrac{2}{6} \\right)^3 =\\dfrac{1}{27}\r\n\\end{align}\\]\r\n\u3088\u3063\u3066, \u6c42\u3081\u308b\u78ba\u7387\u306f\r\n\\[\\begin{align}\r\n\\text{P}( A \\cap B ) & = 1 -\\text{P}( \\overline{A \\cap B} ) \\\\\r\n& = 1 -\\left( \\text{P}( \\overline{A} ) +\\text{P}( \\overline{B} ) -\\text{P}( \\overline{A \\cup B} )\\right) \\\\\r\n& = 1 -\\dfrac{1}{8} -\\dfrac{125}{216} +\\dfrac{1}{27} \\\\\r\n& =\\underline{\\dfrac{1}{3}}\r\n\\end{align}\\]\r\n","protected":false},"excerpt":{"rendered":"(1)\u3000\u8fba\u306e\u9577\u3055\u304c \\(1\\) \u3067\u3042\u308b\u6b63\u56db\u9762\u4f53OABC\u306b\u304a\u3044\u3066\u8fbaAB\u306e\u4e2d\u70b9\u3092D, \u8fbaOC\u306e\u4e2d\u70b9\u3092E\u3068\u3059\u308b. \\(2\\) \u3064\u306e\u30d9\u30af\u30c8\u30eb \\(\\overrightarrow{\\text{DE}}\\) \u3068 \\(\\overrig &hellip; <a href=\"https:\/\/www.roundown.net\/nyushi\/tok201201\/\">\u7d9a\u304d\u3092\u8aad\u3080 <span class=\"meta-nav\">&rarr;<\/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":[61],"tags":[141,68],"class_list":["post-374","post","type-post","status-publish","format-standard","hentry","category-toko_2012","tag-toko","tag-68"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/374","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=374"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/374\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=374"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=374"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=374"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}