{"id":1921,"date":"2021-10-09T09:41:05","date_gmt":"2021-10-09T00:41:05","guid":{"rendered":"https:\/\/www.roundown.net\/nyushi\/?p=1921"},"modified":"2021-10-09T09:41:44","modified_gmt":"2021-10-09T00:41:44","slug":"ykr201603","status":"publish","type":"post","link":"https:\/\/www.roundown.net\/nyushi\/ykr201603\/","title":{"rendered":"\u6a2a\u56fd\u5927\u7406\u7cfb2016\uff1a\u7b2c3\u554f"},"content":{"rendered":"
\n

\u56db\u9762\u4f53 OABC \u304c\u3042\u308a, \\(\\overrightarrow{\\text{OA}} = \\overrightarrow{a}\\) , \\(\\overrightarrow{\\text{OB}} = \\overrightarrow{b}\\) , \\(\\overrightarrow{\\text{OC}} = \\overrightarrow{c}\\) \u3068\u3059\u308b. \u4e09\u89d2\u5f62 ABC \u306e\u91cd\u5fc3\u3092 G \u3068\u3059\u308b.\r\n\u70b9 D , E , P \u3092 \\(\\overrightarrow{\\text{OD}} = 2 \\overrightarrow{b}\\) , \\(\\overrightarrow{\\text{OE}} = 3 \\overrightarrow{c}\\) , \\(\\overrightarrow{\\text{OP}} = 6 \\overrightarrow{\\text{OG}}\\) \u3092\u307f\u305f\u3059\u70b9\u3068\u3057, \u5e73\u9762 ADE \u3068\u76f4\u7dda OP \u306e\u4ea4\u70b9\u3092 Q \u3068\u3059\u308b. \u6b21\u306e\u554f\u3044\u306b\u7b54\u3048\u3088.<\/p>\r\n

    \r\n

  1. (1)<\/strong>\u3000\\(\\overrightarrow{\\text{OQ}}\\) \u3092 \\(\\overrightarrow{a} , \\overrightarrow{b} , \\overrightarrow{c}\\) \u3092\u7528\u3044\u3066\u8868\u305b.<\/p><\/li>\r\n

  2. (2)<\/strong>\u3000\u4e09\u89d2\u5f62 ADE \u306e\u9762\u7a4d\u3092 \\(S _ 1\\) , \u4e09\u89d2\u5f62 QDE \u306e\u9762\u7a4d\u3092 \\(S _ 2\\) \u3068\u3059\u308b\u3068\u304d, \\(\\dfrac{S _ 2}{S _ 1}\\) \u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n

  3. (3)<\/strong>\u3000\u56db\u9762\u4f53 OADE \u306e\u4f53\u7a4d\u3092 \\(V _ 1\\) , \u56db\u9762\u4f53 PQDE \u306e\u4f53\u7a4d\u3092 \\(V _ 2\\) \u3068\u3059\u308b\u3068\u304d, \\(\\dfrac{V _ 2}{V _ 1}\\) \u3092\u6c42\u3081\u3088.<\/p><\/li>\r\n<\/ol>\r\n

    \r\n\r\n

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

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

    \\[\r\n\\overrightarrow{\\text{OP}} = 2 \\left( \\overrightarrow{a} +\\overrightarrow{b} +\\overrightarrow{c} \\right)\r\n\\]\r\nQ \u306f \u7dda\u5206 OP \u4e0a\u306e\u70b9\u306a\u306e\u3067 \\(t \\ ( 0 \\lt t \\lt 1 )\\) \u3092\u7528\u3044\u3066\r\n\\[\r\n\\overrightarrow{\\text{OQ}} = 2 t \\left( \\overrightarrow{a} +\\overrightarrow{b} +\\overrightarrow{c} \\right)\r\n\\]\r\n\u3068\u8868\u305b\u308b.
    \r\n\u307e\u305f\r\n\\[\\begin{align}\r\n\\overrightarrow{\\text{OQ}} & = 2 t \\overrightarrow{a} +t \\cdot 2 \\overrightarrow{b} +\\dfrac{2t}{3} \\cdot 3 \\overrightarrow{c} \\\\\r\n& = 2t \\overrightarrow{\\text{OA}} +t \\overrightarrow{\\text{OD}} +\\dfrac{2t}{3} \\overrightarrow{\\text{OE}}\r\n\\end{align}\\]\r\nQ \u306f \u5e73\u9762 ADE \u4e0a\u306e\u5186\u306a\u306e\u3067\r\n\\[\\begin{align}\r\n2t +t +\\dfrac{2t}{3} & = 1 \\\\\r\n\\text{\u2234} \\quad t = \\dfrac{3}{11}\r\n\\end{align}\\]\r\n\u3088\u3063\u3066\r\n\\[\r\n\\overrightarrow{\\text{OQ}} = \\underline{\\dfrac{6}{11} \\left( \\overrightarrow{a} +\\overrightarrow{b} +\\overrightarrow{c} \\right)}\r\n\\]\r\n

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

    \\[\\begin{align}\r\n\\overrightarrow{\\text{OQ}} & = \\dfrac{6}{11} \\overrightarrow{\\text{OA}} +\\dfrac{3}{11} \\overrightarrow{\\text{OD}} +\\dfrac{2}{11} \\overrightarrow{\\text{OE}} \\\\\r\n& = \\dfrac{6}{11} \\overrightarrow{\\text{OA}} +\\dfrac{5}{11} \\left( \\dfrac{3}{5} \\overrightarrow{\\text{OD}} +\\dfrac{2}{5} \\overrightarrow{\\text{OE}} \\right)\r\n\\end{align}\\]\r\n\u306a\u306e\u3067, DE \u3092 \\(2:3\\) \u3067\u5185\u5206\u3059\u308b\u70b9\u3092 R \u3068\u3059\u308c\u3070, Q \u306f AR \u3092 \\(5:6\\) \u306b\u5185\u5206\u3059\u308b\u70b9\u3067\u3042\u308b.
    \r\n\u3088\u3063\u3066\r\n\\[\r\n\\dfrac{S _ 2}{S _ 1} = \\dfrac{\\text{QR}}{\\text{AR}} = \\underline{\\dfrac{6}{11}}\r\n\\]\r\n

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

    \\[\r\n\\text{OQ} : \\text{QP} = \\dfrac{6}{11} : \\left( 2 -\\dfrac{6}{11} \\right) = 3:8\r\n\\]\r\n\u3088\u3063\u3066\r\n\\[\\begin{align}\r\n\\dfrac{V _ 2}{V _ 1} & = \\dfrac{S_2 \\cdot \\text{QP}}{S_1 \\cdot \\text{OQ}} & = \\dfrac{6 \\cdot 8}{11 \\cdot 3} = \\underline{\\dfrac{16}{11}}\r\n\\end{align}\\]\r\n","protected":false},"excerpt":{"rendered":"\u56db\u9762\u4f53 OABC \u304c\u3042\u308a, \\(\\overrightarrow{\\text{OA}} = \\overrightarrow{a}\\) , \\(\\overrightarrow{\\text{OB}} = \\overrighta … \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":[159],"tags":[162,9],"class_list":["post-1921","post","type-post","status-publish","format-standard","hentry","category-yokokoku_r_2016","tag-162","tag-yokokoku_r"],"_links":{"self":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1921","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=1921"}],"version-history":[{"count":0,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/posts\/1921\/revisions"}],"wp:attachment":[{"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/media?parent=1921"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/categories?post=1921"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/www.roundown.net\/nyushi\/wp-json\/wp\/v2\/tags?post=1921"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}