\\(3\\)\ucc28\uc6d0 \uacf5\uac04\uc5d0 \uc11c\ub85c \ub2e4\ub978 \ub450 \uc810 \\(P,\\) \\(S\\)\uc640 \ubca1\ud130 \\(\\textbf{v}\\)\uac00 \uc8fc\uc5b4\uc84c\ub2e4\uace0 \ud558\uc790. \uadf8\ub9ac\uace0 \uc810 \\(S\\)\ub97c \uc9c0\ub098\uace0 \\(\\textbf{v}\\)\uc640 \ud3c9\ud589\ud55c \uc9c1\uc120\uc744 \\(\\ell\\)\uc774\ub77c\uace0 \ud558\uc790. \uc774\ub54c \\(P\\)\uc640 \\(\\ell\\) \uc0ac\uc774\uc758 \uac70\ub9ac \\(d\\)\ub294 \ub2e4\uc74c\uacfc \uac19\uc740 \ubc29\ubc95\uc73c\ub85c \uad6c\ud560 \uc218 \uc788\ub2e4.<\/p>\n
\ud3c9\ud589\uc0ac\ubcc0\ud615\uc758 \uc778\uc811\ud55c \ub450 \ubcc0\uc774 \uac01\uac01 \\(\\overrightarrow{PS},\\) \\(\\textbf{v}\\)\uc640 \ud3c9\ud589\ud558\uace0, \ub450 \ubcc0\uc758 \uae38\uc774\uac00 \uac01\uac01 \\(\\vert\\overrightarrow{PS}\\lvert,\\) \\(\\lvert\\textbf{v}\\vert\\)\uc640 \uac19\uc744 \ub54c, \uc774 \ud3c9\ud589\uc0ac\ubcc0\ud615\uc758 \ub113\uc774\ub294 \ub450 \ubca1\ud130\uc758 \uc678\uc801\uc758 \ud06c\uae30\uc778 \\(\\lvert \\overrightarrow{PS} \\times \\textbf{v}\\rvert\\)\uc640 \uac19\ub2e4. \uc774\ub54c \uc810 \\(P\\)\uc640 \uc9c1\uc120 \\(\\ell\\) \uc0ac\uc774\uc758 \uac70\ub9ac\ub294 \uc774 \ud3c9\ud589\uc0ac\ubcc0\ud615\uc758 \ub192\uc774\uc640 \uac19\ub2e4. \uadf8\ub7ec\ubbc0\ub85c \ud3c9\ud589\uc0ac\ubcc0\ud615\uc758 \ub192\uc774\ub97c \ud3c9\ud589\uc0ac\ubcc0\ud615\uc758 \ubc11\ubcc0\uc758 \uae38\uc774\ub85c \ub098\ub204\uba74 \ud3c9\ud589\uc0ac\ubcc0\ud615\uc758 \ub192\uc774 \\(d\\)\uc640 \uac19\ub2e4.<\/p>\n
\ubcf4\uae30.<\/span> \ubcf4\uae30\uc758 \ubb38\uc81c\ub97c \ub2e4\ub978 \ubc29\ubc95\uc73c\ub85c \ud480\uc5b4\ubcf4\uc790. \ub77c\uadf8\ub791\uc8fc\uc758 \ubc29\ubc95(method of Lagrange)\uc740 \ubcc0\uc218\uc5d0 \uc81c\ud55c \uc870\uac74\uc774 \uc8fc\uc5b4\uc84c\uc744 \ub54c \uc8fc\uc5b4\uc9c4 \ud568\uc218\uac00 \uadf9\uac12\uc744 \uac16\ub294 \uc810\uc744 \ucc3e\ub294 \ubc29\ubc95\uc774\ub2e4. \ub77c\uadf8\ub791\uc8fc\uc758 \ubc29\ubc95\uc73c\ub85c \ubcf4\uae30\uc758 \ubb38\uc81c\ub97c \ud574\uacb0\ud560 \uc218 \uc788\ub2e4.<\/p>\n \uc810 \\(S\\)\uc640 \uc9c1\uc120 \\(\\ell\\)\uc744 \ubaa8\ub450 \ub3d9\uc77c\ud558\uac8c \ud3c9\ud589\uc774\ub3d9\uc2dc\ucf1c\uc11c \\(S\\)\uac00 \uc6d0\uc810\uc5d0 \ub193\uc774\ub3c4\ub85d \ud558\uc790. \uadf8\ub7ec\uba74 \uc9c1\uc120\uc740 \ub2e4\uc74c\uacfc \uac19\uc774 \ub098\ud0c0\ub0bc \uc218 \uc788\ub2e4. \uc774\uc81c \uc774 \uc810\uacfc \uc6d0\uc810 \uc0ac\uc774\uc758 \uac70\ub9ac\ub97c \uad6c\ud558\uba74 <\/p>\n","protected":false},"excerpt":{"rendered":" \\(3\\)\ucc28\uc6d0 \uacf5\uac04\uc5d0 \uc11c\ub85c \ub2e4\ub978 \ub450 \uc810 \\(P,\\) \\(S\\)\uc640 \ubca1\ud130 \\(\\textbf{v}\\)\uac00 \uc8fc\uc5b4\uc84c\ub2e4\uace0 \ud558\uc790. \uadf8\ub9ac\uace0 \uc810 \\(S\\)\ub97c \uc9c0\ub098\uace0 \\(\\textbf{v}\\)\uc640 \ud3c9\ud589\ud55c \uc9c1\uc120\uc744 \\(\\ell\\)\uc774\ub77c\uace0 \ud558\uc790. \uc774\ub54c \\(P\\)\uc640 \\(\\ell\\) \uc0ac\uc774\uc758 \uac70\ub9ac \\(d\\)\ub294 \ub2e4\uc74c\uacfc \uac19\uc740 \ubc29\ubc95\uc73c\ub85c \uad6c\ud560 \uc218 \uc788\ub2e4. \\(d = \\frac{\\lvert \\overrightarrow{PS} \\times \\textbf{v}\\rvert}{\\lvert\\textbf{v}\\rvert}.\\) \ud3c9\ud589\uc0ac\ubcc0\ud615\uc758 \uc778\uc811\ud55c \ub450 \ubcc0\uc774 \uac01\uac01 \\(\\overrightarrow{PS},\\) \\(\\textbf{v}\\)\uc640 \ud3c9\ud589\ud558\uace0, \ub450 \ubcc0\uc758 \uae38\uc774\uac00 \uac01\uac01 \\(\\vert\\overrightarrow{PS}\\lvert,\\) \\(\\lvert\\textbf{v}\\vert\\)\uc640 \uac19\uc744 \ub54c, \uc774 \ud3c9\ud589\uc0ac\ubcc0\ud615\uc758 \ub113\uc774\ub294 \ub450 \ubca1\ud130\uc758 \uc678\uc801\uc758 \ud06c\uae30\uc778 \\(\\lvert \\overrightarrow{PS}…<\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"_lmt_disableupdate":"","_lmt_disable":"","footnotes":""},"categories":[47,57],"tags":[],"class_list":["post-4584","post","type-post","status-publish","format-standard","hentry","category-calculus-ap","category-linear-algebra"],"_links":{"self":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/posts\/4584","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/comments?post=4584"}],"version-history":[{"count":26,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/posts\/4584\/revisions"}],"predecessor-version":[{"id":4610,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/posts\/4584\/revisions\/4610"}],"wp:attachment":[{"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/media?parent=4584"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/categories?post=4584"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/sasamath.com\/blog\/wp-json\/wp\/v2\/tags?post=4584"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}
\n\uc704 \uacf5\uc2dd\uc744 \uc774\uc6a9\ud558\uc5ec \uc810 \\(S(1,\\,1,\\,5)\\)\uc640 \uc9c1\uc120
\n\\[\\ell \\,: \\quad x=1+t ,\\quad y=3-t ,\\quad z=2t\\]
\n\uc0ac\uc774\uc758 \uac70\ub9ac\ub97c \uad6c\ud574\ubcf4\uc790. \uba3c\uc800
\n\\[\\overrightarrow{PS} = -2\\textbf{j} + 5\\textbf{k}\\]
\n\uc774\uace0
\n\\[\\overrightarrow{PS} \\times \\textbf{v}
\n=
\n\\left\\lvert
\n\\begin{matrix}
\n\\textbf{i} & \\textbf{j} & \\textbf{k} \\\\
\n0 & -2 & 5 \\\\
\n1 & -1 & 2
\n\\end{matrix}
\n\\right\\rvert
\n= \\textbf{i} + 5\\textbf{j} + 2\\textbf{k}
\n\\]
\n\uc774\ubbc0\ub85c \\(S\\)\uc640 \\(\\ell\\) \uc0ac\uc774\uc758 \uac70\ub9ac\ub294 \ub2e4\uc74c\uacfc \uac19\ub2e4.
\n\\[d = \\frac{\\sqrt{1+25+4}}{\\sqrt{1+1+4}} = \\sqrt{5} .\\tag*{\\(\\square\\)}\\]\n<\/p>\n<\/div>\n
\n\\[L : \\quad x = t ,\\quad y = 2-t ,\\quad z = 2t-5 .\\]
\n\uc774 \uc9c1\uc120\uacfc \uc6d0\uc810 \uc0ac\uc774\uc758 \uac70\ub9ac\uac00 \ucd5c\uc18c\uac00 \ub418\ub3c4\ub85d \ud558\ub294 \uc810\uc758 \uc88c\ud45c \\((x,\\,y,\\,z)\\)\ub97c \uad6c\ud574\uc57c \ud55c\ub2e4. \uc6d0\uc810\uacfc\uc758 \uac70\ub9ac\uac00 \ucd5c\uc18c\uc778 \uc810\uc744 \ucc3e\ub294\ub2e4\ub294 \uac83\uc740 \ud568\uc218
\n\\[f(x,\\,y,\\,z) = x^2 + y^2 + z^2\\]
\n\uc758 \uac12\uc774 \ucd5c\uc18c\uac00 \ub418\ub3c4\ub85d \ud558\ub294 \uc810\uc758 \uc88c\ud45c \\((x,\\,y,\\,z)\\)\ub97c \uad6c\ud558\ub294 \uac83\uacfc \uac19\ub2e4. \uc774\uc81c \uc9c1\uc120 \\(L\\)\uc744 \uc774\uc6a9\ud558\uc5ec \uc81c\ud55c \uc870\uac74\uc744 \ub9cc\ub4e4\uc790. \\(L\\)\uc758 \ucc98\uc74c \ub450 \ub4f1\uc2dd\uc744 \uc5f0\ub9bd\ud558\uba74
\n\\[y = 2-x\\tag{2}\\]
\n\uac00 \ub418\uba70, \\(L\\)\uc758 \uccab \ub4f1\uc2dd\uacfc \ub9c8\uc9c0\ub9c9 \ub4f1\uc2dd\uc744 \uc5f0\ub9bd\ud558\uba74
\n\\[z =2x-5 \\tag{3}\\]
\n\ub97c \uc5bb\ub294\ub2e4. (2)\uc640 (3)\uc744 \uc774\uc6a9\ud558\uae30 \uc704\ud558\uc5ec \ub2e4\uc74c \ub450 \ud568\uc218\ub97c \ub3c4\uc785\ud55c\ub2e4.
\n\\[\\begin{gather}
\ng(x,\\,y,\\,z) = x+y-2 ,\\\\[6pt]
\nh(x,\\,y,\\,z) = 2x-z-5 .
\n\\end{gather}\\]
\n\ub450 \ud568\uc218\uc758 \uac12\uc774 \ubaa8\ub450 \\(0\\)\uc774 \ub418\ub3c4\ub85d \ud558\ub294 \uc810\ub4e4\uc758 \ubaa8\uc784\uc774 \uace7 \uc9c1\uc120 \\(L\\)\uc774 \ub41c\ub2e4. \uadf8\ub7ec\ubbc0\ub85c \uc6b0\ub9ac\ub294 \ubcc0\uc218\uac00 \ub450 \uc81c\ud55c\uc870\uac74
\n\\[\\begin{gather}
\ng(x,\\,y,\\,z) =0, \\\\[6pt]
\nh(x,\\,y,\\,z) =0
\n\\end{gather}\\]
\n\uc744 \ubaa8\ub450 \ub9cc\uc871\uc2dc\ud0ac \ub54c \\(f(x,\\,y,\\,z)\\)\uc758 \uadf9\uac12\uc744 \uad6c\ud574\uc57c \ud55c\ub2e4. \ub77c\uadf8\ub791\uc8fc\uc758 \ubc29\ubc95\uc744 \uc774\uc6a9\ud558\uc790.
\n\\[\\nabla f = \\lambda \\nabla g + \\mu \\nabla h\\tag{4}\\]
\n\ub97c \ub9cc\uc871\uc2dc\ud0a4\ub294 \uc0c1\uc218 \\(\\lambda ,\\) \\(\\mu\\)\uc640 \\((x,\\,y,\\,z)\\)\ub97c \uad6c\ud574\uc57c \ud55c\ub2e4. (4)\uc5d0 \uc758\ud558\uc5ec
\n\\[2x\\,\\textbf{i} + 2y\\,\\textbf{j} + 2z\\,\\textbf{k} = \\lambda (\\textbf{i} + \\textbf{j}) + \\mu (2 \\textbf{i} – \\textbf{k})\\]
\n\uc989
\n\\[\\begin{cases}
\n2x = \\lambda + 2\\mu \\\\[6pt]
\n2y = \\lambda \\\\[6pt]
\n2z = – \\mu
\n\\end{cases}\\]
\n\ub97c \uc5bb\uc73c\uba70, \uc774 \uc2dd\uc744 \ud1b5\ud558\uc5ec
\n\\[x-y+2z=0 \\tag{5}\\]
\n\uc744 \uc5bb\ub294\ub2e4. \uc9c1\uc120 \\(L\\)\uc758 \ubc29\uc815\uc2dd\uc744 \uc774\uc6a9\ud558\uc5ec (5)\ub97c \\(t\\)\uc5d0 \ub300\ud55c \uc2dd\uc73c\ub85c \ubcc0\ud615\ud558\uba74
\n\\[t-(2-t)+2(2t-5)=0\\]
\n\uc774 \ub418\uba70, \uc774 \uc2dd\uc744 \ud480\uba74 \\(t=2\\)\ub97c \uc5bb\ub294\ub2e4. \ub2e4\uc2dc \\(t=2\\)\ub97c \uc9c1\uc120\uc758 \ubc29\uc815\uc2dd\uc5d0 \ub300\uc785\ud558\uba74
\n\\[x=2 ,\\,\\, y=0 ,\\,\\, z=-1\\]
\n\uc744 \uc5bb\ub294\ub2e4. \uc989 \\((2,\\,0,\\,-1)\\)\uc740 \uc9c1\uc120 \uc704\uc758 \uc810 \uc911\uc5d0\uc11c \uc6d0\uc810\uc5d0 \uac00\uc7a5 \uac00\uae4c\uc6b4 \uc810\uc758 \ud6c4\ubcf4\uc774\ub2e4. \ud55c\ud3b8 \\(3\\)\ucc28\uc6d0 \uacf5\uac04\uc5d0\uc11c \uc9c1\uc120\uc740 \ub2eb\ud78c \uc9d1\ud569\uc774\uace0, \\(t \\,\\to\\, \\pm \\infty\\)\uc77c \ub54c \uc9c1\uc120 \uc704\uc758 \uc810\uacfc \uc6d0\uc810 \uc0ac\uc774\uc758 \uac70\ub9ac\ub294 \ubb34\ud55c\ub300\ub85c \ubc1c\uc0b0\ud558\ubbc0\ub85c, \\((2,\\,0,\\,-1)\\)\uc740 \uc9c1\uc120 \uc704\uc758 \uc810 \uc911\uc5d0\uc11c \uc6d0\uc810\uacfc \uac00\uc7a5 \uac00\uae4c\uc6b4 \uc810\uc774\ub2e4.<\/p>\n
\n\\[d = \\sqrt{2^2 + 0^2 + (-1)^2} = \\sqrt{5}\\]
\n\ub85c\uc11c, \uc55e\uc758 \ud480\uc774\uc758 \uacb0\uacfc\uc640 \ub3d9\uc77c\ud55c \uac12\uc744 \uc5bb\ub294\ub2e4.
\n<\/span><\/p>\n<\/div>\n