{"id":80743,"date":"2024-03-05T20:49:20","date_gmt":"2024-03-05T20:49:20","guid":{"rendered":"https:\/\/science-hub.click\/%E7%B7%9A%E3%81%A8%E5%B9%B3%E9%9D%A2%E3%81%AE%E3%83%A1%E3%83%BC%E3%83%88%E3%83%AB%E7%89%B9%E6%80%A7-%E5%AE%9A%E7%BE%A9\/"},"modified":"2024-03-05T20:49:20","modified_gmt":"2024-03-05T20:49:20","slug":"%E7%B7%9A%E3%81%A8%E5%B9%B3%E9%9D%A2%E3%81%AE%E3%83%A1%E3%83%BC%E3%83%88%E3%83%AB%E7%89%B9%E6%80%A7-%E5%AE%9A%E7%BE%A9","status":"publish","type":"post","link":"https:\/\/science-hub.click\/?p=80743","title":{"rendered":"\u7dda\u3068\u5e73\u9762\u306e\u30e1\u30fc\u30c8\u30eb\u7279\u6027 – \u5b9a\u7fa9"},"content":{"rendered":"

\u5c0e\u5165<\/h2>

\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u5e7e\u4f55\u5b66\u3001\u3064\u307e\u308a\u3001\u8ddd\u96e2\u3068\u30b9\u30ab\u30e9\u30fc\u7a4d\u304c\u4e0e\u3048\u3089\u308c\u308b\u5e73\u9762\u3068\u7a7a\u9593\u3067\u306f\u3001\u7dda\u3068\u5e73\u9762\u306b\u306f<\/b>\u8a08\u91cf\u7279\u6027<\/b>\u304c\u3042\u308a\u3001\u70b9<\/a><\/span>\u3068\u30d9\u30af\u30c8\u30eb (\u6cd5\u7dda) \u3092<\/a><\/span>\u4f7f\u7528\u3057\u3066\u7279\u5fb4\u4ed8\u3051\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002\u307e\u305f\u3001\u7279\u5b9a\u306e\u70b9\u304b\u3089\u305d\u308c\u3089\u3092\u5206\u96e2\u3059\u308b\u8ddd\u96e2\u3092\u8a08\u7b97\u3057\u305f\u308a\u30012 \u3064\u306e\u76f4\u7dda\u307e\u305f\u306f 2 \u3064\u306e\u5e73\u9762\u3092\u5206\u96e2\u3059\u308b\u8ddd\u96e2\u3092\u8a08\u7b97\u3057\u305f\u308a\u3059\u308b\u3053\u3068\u3082\u3067\u304d\u307e\u3059\u3002 2 \u672c\u306e\u76f4\u7dda\u307e\u305f\u306f 2 \u3064\u306e\u5e73\u9762\u306b\u3088\u3063\u3066\u5f62\u6210\u3055\u308c\u308b\u89d2\u5ea6<\/a><\/span>\u3092\u8a08\u7b97\u3059\u308b\u3053\u3068\u3082\u3067\u304d\u307e\u3059\u3002<\/p>

\u3053\u306e\u8a18\u4e8b\u3067\u306f\u3001\u3059\u3079\u3066\u306e\u5ea7\u6a19\u304c\u8868\u73fe\u3055\u308c\u308b\u6b63\u898f\u76f4\u4ea4\u57fa\u6e96\u30d5\u30ec\u30fc\u30e0\u3092\u5e73\u9762\u307e\u305f\u306f\u7a7a\u9593\u306b\u63d0\u4f9b\u3057\u307e\u3057\u305f\u3002\u5e73\u9762 y \u306e\u3059\u3079\u3066\u306e\u7dda\u306b\u306fux + vy + h = 0 \u3068\u3044\u3046<\/i>\u30bf\u30a4\u30d7\u306e\u65b9\u7a0b\u5f0f\u304c\u3042\u308a\u3001 ( u<\/i> , v<\/i> ) \u306f (0, 0) \u3068\u306f\u7570\u306a\u308a\u3001\u7a7a\u9593\u306e\u3059\u3079\u3066\u306e<\/a><\/span>\u5e73\u9762\u306b\u306fux + vy + wz + \u3068\u3044\u3046<\/i>\u5f62\u5f0f\u306e\u65b9\u7a0b\u5f0f\u304c\u3042\u308a\u307e\u3059\u3002 h = 0<\/i> ( u, v, w<\/i> ) \u306f (0, 0, 0) \u3068\u306f\u7570\u306a\u308a\u307e\u3059<\/p>

\n\"\u7dda\u3068\u5e73\u9762\u306e\u30e1\u30fc\u30c8\u30eb\u7279\u6027<\/figure>

\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u5e73\u9762\u4e0a\u306e\u7dda<\/h2>

\u7dda\u306b\u5bfe\u3059\u308b\u6cd5\u7dda\u30d9\u30af\u30c8\u30eb<\/span><\/h3>

M<\/i> ( x<\/i> , y<\/i> )<\/span>\u3092\u76f4\u7dda D \u4e0a\u306e\u70b9\u3068\u3057\u3001\u6b63\u898f\u76f4\u4ea4\u5ea7\u6a19\u7cfb\u306e\u65b9\u7a0b\u5f0f\u306f\u6b21\u306e\u3088\u3046\u306b\u4e0e\u3048\u3089\u308c\u307e\u3059<\/span>\u3002 <\/p>

$$ {(1) \\qquad ux + vy + h = 0\\,} $$<\/div><\/center>

M<\/i> 0<\/sub> ( x<\/i> 0<\/sub> , y<\/i> 0<\/sub> )<\/span> D \u306e\u7279\u5b9a\u306e\u70b9\u3001\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002 <\/p>

$$ {(2) \\qquad ux_0 + vy_0 + h = 0\\,} $$<\/div><\/center>

(1) \u304b\u3089 (2) \u3092\u5f15\u304f\u3068\u3001\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002 <\/p>

$$ {u(x-x_0) + v(y-y_0)= 0\\,} $$<\/div><\/center>

\u6ce8\u76ee\u3059\u308b

$$ {\\scriptstyle \\overrightarrow{N}\\,} $$<\/div> \u3001\u5ea7\u6a19\u30d9\u30af\u30c8\u30eb ( u, v<\/i> ) \u3068\u3057\u3066\u3001(1) \u3092\u6b21\u306e\u3088\u3046\u306b\u8868\u3057\u307e\u3059\u3002 <\/p>
$$ {\\overrightarrow{N} . \\overrightarrow{M_0M}=0\\,} $$<\/div><\/center>

\u3057\u305f\u304c\u3063\u3066\u3001\u65b9\u7a0b\u5f0fu<\/i> x<\/i> + v<\/i> y<\/i> + h<\/i> = 0<\/span>\u306e\u76f4\u7dda\u306f\u200b\u200b\u30d9\u30af\u30c8\u30eb\u306b\u76f4\u4ea4\u3057\u307e\u3059\u3002

$$ {\\scriptstyle \\overrightarrow{N}\\,} $$<\/div> \u3002\u30d9\u30af\u30c8\u30eb
$$ {\\scriptstyle \\overrightarrow{N}\\,} $$<\/div>\u7ddaD\u306b\u5782\u76f4\u306a\u30d9\u30af\u30c8\u30eb\u3068\u547c\u3070\u308c\u307e\u3059<\/p>

\u70b9\u3092\u901a\u308a\u3001\u6307\u5b9a\u3055\u308c\u305f\u975e\u30bc\u30ed\u30d9\u30af\u30c8\u30eb\u306b\u76f4\u4ea4\u3059\u308b\u7dda<\/span><\/h3>

\u70b9M<\/i> ( x<\/i> , y<\/i> )<\/span>\u3068\u30d9\u30af\u30c8\u30eb\u3092\u8003\u3048\u307e\u3059\u3002

$$ {\\scriptstyle \\overrightarrow{N}(u,v)} $$<\/div>\u30bc\u30ed\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u70b9 M \u306f\u3001 M<\/i> 0<\/sub> ( x<\/i> 0<\/sub> , y<\/i> 0<\/sub> )<\/span>\u3092\u901a\u308a\u3001 \u306b\u76f4\u4ea4\u3059\u308b\u76f4\u7dda D \u306b\u5c5e\u3057\u307e\u3059\u3002
$$ {\\scriptstyle \\overrightarrow{N}} $$<\/div> \u3001\u6b21\u306e\u5834\u5408\u306b\u9650\u308a\u307e\u3059\u3002 <\/p>
$$ {\\overrightarrow{N} . \\overrightarrow{M_0M}=0} $$<\/div><\/center><\/dd><\/dl>

M<\/i> 0<\/sub> ( x<\/i> 0<\/sub> , y<\/i> 0<\/sub> )<\/span>\u3092\u901a\u308a\u3001\u305d\u308c\u306b\u76f4\u4ea4\u3059\u308b\u76f4\u7dda D

$$ {\\scriptstyle \\overrightarrow{N}} $$<\/div>\u3057\u305f\u304c\u3063\u3066\u3001\u6b21\u306e\u65b9\u7a0b\u5f0f\u304c\u3042\u308a\u307e\u3059:: <\/p>
$$ {u(x-x_0) + v(y-y_0)= 0\\,} $$<\/div><\/center><\/dd><\/dl>

\u70b9M<\/i> ( x<\/i> , y<\/i> )<\/span>\u304b\u3089\u65b9\u7a0b\u5f0fu<\/i> x<\/i> + v<\/i> y<\/i> + h<\/i> = 0<\/span>\u306e\u76f4\u7dda\u307e\u3067\u306e\u4ee3\u6570\u7684\u8ddd\u96e2<\/span><\/h3>

H \u3092M<\/i> ( x<\/i> , y<\/i> )<\/span>\u306e D \u3078\u306e\u5c04\u5f71\u3068\u3057\u307e\u3059\u3002

$$ {\\overrightarrow{HM}} $$<\/div> D\u306b\u76f4\u4ea4\u3059\u308b\u3002<\/p>

D \u306b\u5782\u76f4\u3067<\/a><\/span>M \u3092\u901a\u308b\u76f4\u7dda\u304c\u30d9\u30af\u30c8\u30eb\u306e\u65b9\u5411\u306b\u5411\u3044\u3066\u3044\u308b

$$ {\\scriptstyle \\overrightarrow{N}(u,v)} $$<\/div> \u3001M \u3068 D \u306e\u9593\u306e\u4ee3\u6570\u7684\u8ddd\u96e2\u304c\u6b21\u306e\u5f0f\u3067\u4e0e\u3048\u3089\u308c\u308b\u3053\u3068\u3092\u793a\u3057\u307e\u3059\u3002 <\/p>
$$ {d_a(H,M) = \\frac{ux+vy+h}\\sqrt{u^2 + v^2}} $$<\/div><\/center><\/dd><\/dl>

\u7d76\u5bfe\u5024<\/a><\/span>\u3067: <\/p>

$$ {\\|\\overrightarrow{HM}\\| = \\frac{|ux+vy+h|}\\sqrt{u^2 + v^2}} $$<\/div><\/center><\/dd><\/dl>

\u76f4\u7dda\u3068\u5742\u9053<\/span><\/h3>

v \u304c<\/i>\u30bc\u30ed\u4ee5\u5916\u306e\u5834\u5408\u3001\u65b9\u7a0b\u5f0fu<\/i> x<\/i> + v<\/i> y<\/i> + h<\/i> = 0<\/span>\u3092\u542b\u3080\u7dda D \u306b\u306f\u3001 m<\/i> x<\/i> + b<\/i> = y<\/i><\/span>\u306e\u5f62\u5f0f\u306e\u65b9\u7a0b\u5f0f\u304c\u542b\u307e\u308c\u307e\u3059\u3002 <\/p>

$$ {m= -\\frac{u}{v}\\,} $$<\/div><\/dd><\/dl>

\u305d\u3057\u3066<\/p>

$$ {b= -\\frac{h}{v}\\,} $$<\/div><\/dd><\/dl>

\u7dda\u306e\u50be\u304d\u306f\u5b9f\u969b\u306e\u3082\u306e\u3067\u3059<\/p>

$$ {m = \\tan(\\alpha)\\,} $$<\/div><\/center><\/dd><\/dl>

\u89d2\u5ea6 \u03b1 \u306f\u3001\u6a2a\u8ef8\u3068\u7dda D \u306e\u9593\u306e\u89d2\u5ea6\u3092\u8868\u3057\u307e\u3059\u3002<\/p>

\n\"\u7dda\u3068\u5e73\u9762\u306e\u30e1\u30fc\u30c8\u30eb\u7279\u6027<\/figure>

\u76f4\u7dda\u306e\u6b63\u898f\u65b9\u7a0b\u5f0f<\/a><\/span><\/span><\/h3>

\u30d9\u30f3\u30c1\u30de\u30fc\u30af\u3067\u306f

$$ {\\scriptstyle (O, \\vec i, \\vec j)} $$<\/div> \u3001\u6ce8\u610f\u3057\u307e\u3057\u3087\u3046
$$ {\\scriptstyle \\overrightarrow{N}(cos\\varphi,sin\\varphi)} $$<\/div>\u7dda D \u306b\u5782\u76f4\u306a\u3001O \u304b\u3089 D \u306e\u65b9\u5411\u306e\u5358\u4f4d\u30d9\u30af\u30c8\u30eb\u3001\u5024
$$ { \\varphi} $$<\/div>\u6b21\u306b\u89d2\u5ea6\u3092\u8868\u3057\u307e\u3059
$$ {\\scriptstyle (\\vec i, \\overrightarrow N)} $$<\/div> \u3002\u4e00\u65b9\u3001\u53c2\u7167\u30d5\u30ec\u30fc\u30e0\u306e\u539f\u70b9O<\/i>\u3068\u7dda D \u306e\u9593\u306e\u8ddd\u96e2p \u306b<\/i><\/span>\u6ce8\u76ee\u3057\u307e\u3059\u3002<\/p>

\u5f0f (1) \u306f\u6b21\u306e\u3088\u3046\u306b\u66f8\u304b\u308c\u307e\u3059\u3002 <\/p>

$$ {x\\cos\\varphi+y\\sin\\varphi-p=0} $$<\/div><\/center>

2\u672c\u306e\u7dda\u306e\u89d2\u5ea6<\/span><\/h3>

D \u3068 D’ \u3092\u65b9\u7a0b\u5f0f\u306e 2 \u3064\u306e\u76f4\u7dda\u3068\u3059\u308b<\/p>

$$ {(D): ux+vy+h = 0\\,} $$<\/div><\/center><\/dd>
$$ {(D’): u’x+v’y+h’ = 0\\,} $$<\/div><\/center><\/dd><\/dl>

2 \u672c\u306e\u7dda\u306b\u3088\u3063\u3066\u5f62\u6210\u3055\u308c\u308b\u89d2\u5ea6\u306f\u3001\u305d\u306e\u63a5\u7dda\u306b\u3088\u3063\u3066\u308f\u304b\u308a\u307e\u3059\u3002 <\/p>

$$ {\\tan(D,D’)= \\tan(\\overrightarrow{N},\\overrightarrow{N’}) = \\frac{uv’-u’v}{uu’+vv’}} $$<\/div><\/center>

\u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u7a7a\u9593\u306e\u5e73\u9762<\/h2>

\u5e73\u9762\u306b\u76f4\u4ea4\u3059\u308b\u30d9\u30af\u30c8\u30eb<\/span><\/h3>

M<\/i> ( x<\/i> , y<\/i> , z<\/i> ) \u3092<\/span>\u5e73\u9762 P \u4e0a\u306e\u70b9\u3068\u3057\u3001\u305d\u306e\u6b63\u898f\u76f4\u4ea4\u5ea7\u6a19\u7cfb\u306e\u65b9\u7a0b\u5f0f\u306f\u6b21\u306e\u5f0f\u3067\u4e0e\u3048\u3089\u308c\u307e\u3059\u3002 <\/p>

$$ {(1bis) \\qquad ux+vy+wz+h=0} $$<\/div><\/center>

M<\/i> 0<\/sub> ( x<\/i> 0<\/sub> , y<\/i> 0<\/sub> , z<\/i> 0<\/sub> )<\/span>\u306b\u3064\u3044\u3066\u306f\u3001P \u306e\u7279\u5b9a\u306e\u70b9\u3092\u53d6\u5f97\u3057\u307e\u3059\u3002 <\/p>

$$ {(2bis) \\qquad ux_0+vy_0+wz_0+h = 0} $$<\/div><\/center>

(1bis) \u304b\u3089 (2bis) \u3092\u5f15\u304f\u3068\u3001\u6b21\u304c\u5f97\u3089\u308c\u307e\u3059\u3002 <\/p>

$$ {u(x-x_0)+v(y-y_0)+w(z-z_0) = 0\\,} $$<\/div><\/center>

\u6ce8\u76ee\u3059\u308b

$$ {\\overrightarrow{N}} $$<\/div> \u3001\u5ea7\u6a19\u30d9\u30af\u30c8\u30eb ( u,, v, w<\/i> ) \u306f\u3001(1bis) \u3092\u6b21\u306e\u3088\u3046\u306b\u8868\u3057\u307e\u3059\u3002 <\/p>
$$ {\\overrightarrow{N} . \\overrightarrow{M_0M}=0} $$<\/div><\/center>

\u3057\u305f\u304c\u3063\u3066\u3001\u65b9\u7a0b\u5f0fu<\/i> x<\/i> + v<\/i> y<\/i> + w<\/i> z<\/i> + h<\/i> = 0<\/span>\u3092\u6301\u3064\u5e73\u9762 P \u306f\u30d9\u30af\u30c8\u30eb\u306b\u76f4\u4ea4\u3057\u307e\u3059\u3002

$$ {\\overrightarrow{N}(u,v,w)} $$<\/div>\u3053\u306e\u30d9\u30af\u30c8\u30eb\u3092\u5e73\u9762 P \u306b\u5782\u76f4\u306a\u30d9\u30af\u30c8\u30eb\u3068\u547c\u3073\u307e\u3059\u3002<\/p>

\u70b9\u3092\u901a\u308a\u3001\u6307\u5b9a\u3055\u308c\u305f\u975e\u30bc\u30ed\u30d9\u30af\u30c8\u30eb\u306b\u76f4\u4ea4\u3059\u308b\u5e73\u9762<\/span><\/h3>

\u305d\u308c\u3068\u3082\u30dd\u30a4\u30f3\u30c8\u304b

$$ {M(x,y,z)\\,} $$<\/div>\u305d\u3057\u3066\u30d9\u30af\u30c8\u30eb
$$ {\\scriptstyle \\overrightarrow{N}(u,v,w)\\,} $$<\/div>\u30bc\u30ed\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002\u70b9 M \u306f\u5e73\u9762 P \u306b\u5c5e\u3057\u3066\u304a\u308a\u3001
$$ {M_0(x_0,y_0, y_0)\\,} $$<\/div>\u305d\u3057\u3066\u76f4\u4ea4\u3059\u308b
$$ {\\scriptstyle \\overrightarrow{N}\\,} $$<\/div> \u3001\u6b21\u306e\u5834\u5408\u306b\u9650\u308a\u307e\u3059\u3002 <\/p>
$$ {\\overrightarrow{N} . \\overrightarrow{M_0M}=0\\,} $$<\/div><\/center><\/dd><\/dl>

M<\/i> 0<\/sub> ( x<\/i> 0<\/sub> , y<\/i> 0<\/sub> , z<\/i> 0<\/sub> )<\/span>\u3092\u901a\u308a\u3001\u305d\u308c\u306b\u76f4\u4ea4\u3059\u308b\u5e73\u9762 P

$$ {\\scriptstyle \\overrightarrow{N}\\,} $$<\/div>\u3057\u305f\u304c\u3063\u3066\u3001\u6b21\u306e\u65b9\u7a0b\u5f0f\u304c\u3042\u308a\u307e\u3059:: <\/p>
$$ {u(x-x_0) + v(y-y_0) + w(z-z_0)= 0\\,} $$<\/div><\/center><\/dd><\/dl>

\u70b9M<\/i> ( x<\/i> , y<\/i> , z<\/i> )<\/span>\u304b\u3089\u5e73\u9762 P \u307e\u3067\u306e\u4ee3\u6570\u7684\u8ddd\u96e2 (\u5f0fu<\/i> x<\/i> + v<\/i> y<\/i> + w<\/i> z<\/i> + h<\/i> = 0)<\/span><\/span><\/h3>

H \u3092M<\/i> ( x<\/i> , y<\/i> , z<\/i> )<\/span>\u306e P \u3078\u306e\u5c04\u5f71\u3068\u3057\u307e\u3059\u3002

$$ {\\overrightarrow{HM}} $$<\/div> P\u306b\u76f4\u4ea4\u3059\u308b\u3002<\/p>

P \u306b\u5782\u76f4\u3067 M \u3092\u901a\u308b\u7dda\u304c\u30d9\u30af\u30c8\u30eb\u306e\u65b9\u5411\u306b\u5411\u3044\u3066\u3044\u308b

$$ {\\scriptstyle \\overrightarrow{N}(u,v,w)} $$<\/div> \u3001M \u3068 P \u306e\u9593\u306e\u4ee3\u6570\u7684\u8ddd\u96e2\u304c\u6b21\u306e\u5f0f\u3067\u4e0e\u3048\u3089\u308c\u308b\u3053\u3068\u3092\u793a\u3057\u307e\u3059\u3002 <\/p>
$$ {d_a(H,M) = \\frac{ux+vy+wz+h}\\sqrt{u^2 + v^2+w^2}} $$<\/div><\/center><\/dd><\/dl>

\u7d76\u5bfe<\/a><\/span>\u5024: <\/p>

$$ {\\|\\overrightarrow{HM}\\| = \\frac{|ux+vy+wz+h|}\\sqrt{u^2 + v^2+w^2}} $$<\/div><\/center><\/dd><\/dl>

2 \u3064\u306e\u5e73\u9762\u306e\u89d2\u5ea6<\/span><\/h3>

(P) \u3068 (P’) \u3092 2 \u3064\u306e\u65b9\u7a0b\u5f0f\u5e73\u9762\u3068\u3057\u307e\u3059\u3002 <\/p>

$$ {(P)\u00a0: ux+vy+wz+h = 0\\,} $$<\/div><\/center>
$$ {(P’)\u00a0: u’x+v’y+w’z+h’ = 0\\,} $$<\/div><\/center>

\u5e7e\u4f55\u5b66\u7684\u306a\u89d2\u5ea6( P<\/i> \u3001 P<\/i> ‘)<\/span>\u306f\u3001\u6cd5\u7dda\u30d9\u30af\u30c8\u30eb\u306e\u89d2\u5ea6\u3092\u4f7f\u7528\u3057\u3066\u6c7a\u5b9a\u3055\u308c\u307e\u3059\u3002

$$ {(\\overrightarrow{N},\\overrightarrow{N’})} $$<\/div><\/p>
$$ {\\cos(P,P’) = |\\cos(\\overrightarrow{N},\\overrightarrow{N’})|=\\frac{|uu’+vv’+ww’|}{\\sqrt{u^2+v^2+w^2}\\times\\sqrt{u’^2+v’^2+w’^2}}} $$<\/div><\/center>
\n\"\u7dda\u3068\u5e73\u9762\u306e\u30e1\u30fc\u30c8\u30eb\u7279\u6027<\/figure>

\u5782\u76f4\u9762<\/span><\/h3>

\u6cd5\u7dda\u30d9\u30af\u30c8\u30eb\u304c\u6b21\u306e\u5834\u5408\u3001\u5e73\u9762 (P) \u3068 (P’) \u306f\u5782\u76f4\u306b\u306a\u308a\u307e\u3059\u3002

$$ {\\overrightarrow{N}} $$<\/div>\u305d\u3057\u3066
$$ {\\overrightarrow{N’}\\,} $$<\/div>\u306f\u76f4\u4ea4\u3057\u3066\u3044\u307e\u3059\u3002\u3064\u307e\u308a\u3001 <\/p>
$$ {uu’+vv’+ww’ = 0\\,} $$<\/div><\/center>

\u8a08\u753b\u3068\u884c\u5217\u5f0f\u306e\u65b9\u7a0b\u5f0f<\/span><\/h3>

1 \u3064\u306e\u70b9\u3068 2 \u3064\u306e\u975e\u540c\u4e00\u7dda\u4e0a\u306e\u30d9\u30af\u30c8\u30eb\u306b\u3088\u3063\u3066\u5b9a\u7fa9\u3055\u308c\u308b\u5e73\u9762<\/span><\/h4>

\u70b9M<\/i> 0<\/sub> ( x<\/i> 0<\/sub> , y<\/i> 0<\/sub> , z<\/i> 0<\/sub> )<\/span>\u3068 2 \u3064\u306e\u30d9\u30af\u30c8\u30eb\u3092\u8003\u3048\u307e\u3059\u3002

$$ {\\vec V_1} $$<\/div>\u305d\u3057\u3066
$$ {\\vec V_2} $$<\/div>\u975e\u5171\u7dda\u7684\u3002\u70b9 M (x, y, z) \u306f\u3001 M<\/i> 0<\/sub> ( x<\/i> 0<\/sub> , y<\/i> 0<\/sub> , z<\/i> 0<\/sub> )<\/span>\u3068\u305d\u306e\u65b9\u5411\u3092\u901a\u308b\u5e73\u9762 P \u306b\u5c5e\u3057\u307e\u3059\u3002
$$ {\\vec V_1} $$<\/div>\u305d\u3057\u3066
$$ {\\vec V_2} $$<\/div>\u6b21\u306e\u3088\u3046\u306a 2 \u3064\u306e\u5b9f\u6570 \u03bb \u3068 \u03bc \u304c\u5b58\u5728\u3059\u308b\u5834\u5408\u306b\u9650\u308a\u3001
$$ {\\overrightarrow{MM_0} = \\lambda \\vec V_1 + \\mu \\vec V_2} $$<\/div> \u3002\u3053\u306e\u7b49\u5f0f\u306f\u6b21\u306e\u3053\u3068\u3092\u8868\u3057\u307e\u3059
$$ {\\overrightarrow{MM_0},\\vec V_1,\\vec V_2} $$<\/div>\u306f\u540c\u4e00\u5e73\u9762\u4e0a\u306b\u3042\u308a\u307e\u3059\u3002<\/p>

\u3053\u308c\u3089 3 \u3064\u306e\u30d9\u30af\u30c8\u30eb\u306e\u6df7\u5408\u7a4d\u3092\u884c\u5217\u5f0f\u306e\u5f62\u5f0f\u3067\u8868\u3059\u3068\u3001\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002 <\/p>

$$ { \\det(\\overrightarrow{MM_0},\\vec V_1(a_1,b_1,c_1),\\vec V_2(a_2,b_2,c_2))=0 } $$<\/div><\/dd><\/dl>

\u305d\u306e\u65b9\u7a0b\u5f0f\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002 <\/p>

$$ {\\begin{vmatrix} x-x_0 & a_1 &a_2\\\\ y-y_0 & b_1 &b_2\\\\ z-z_0 & c_1 &c_2 \\end{vmatrix} = (b_1c_2 – c_1b_2)(x-x_0) + (c_1a_2 – a_1c_2)(y-y_0) + (a_1b_2 – b_1a_2)(z-z_0) = 0 } $$<\/div><\/dd><\/dl>

\u3053\u308c\u306fu<\/i> x<\/i> + v<\/i> y<\/i> + w<\/i> z<\/i> + h<\/i> = 0 \u306e<\/span>\u5f62\u5f0f\u3067\u66f8\u304f\u3053\u3068\u304c\u3067\u304d\u307e\u3059\u3002<\/p>

2 \u3064\u306e\u70b9\u3068\u30d9\u30af\u30c8\u30eb\u306b\u3088\u3063\u3066\u5b9a\u7fa9\u3055\u308c\u308b\u5e73\u9762<\/span><\/h4>

2 \u3064\u306e\u70b9M<\/i> 1<\/sub> ( x<\/i> 1<\/sub> , y<\/i> 1<\/sub> , z<\/i> 1<\/sub> )\u3001 M<\/i> 2<\/sub> ( x<\/i> 2<\/sub> , y<\/i> 2<\/sub> , z<\/i> 2<\/sub> )<\/span>\u3068\u30d9\u30af\u30c8\u30eb\u3092\u8003\u3048\u307e\u3059\u3002

$$ {\\vec V_1(a,b,c)} $$<\/div>\u3068\u975e\u5171\u7dda\u7684
$$ {\\overrightarrow{M_1M_2}} $$<\/div> \u3002<\/p>

\u70b9 M \u306f\u3001 M<\/i> 1<\/sub> ( x<\/i> 1<\/sub> , y<\/i> 1<\/sub> , z<\/i> 1<\/sub> )\u3001 M<\/i> 2<\/sub> ( x<\/i> 2<\/sub> , y<\/i> 2<\/sub> , z<\/i> 2<\/sub> )<\/span>\u304a\u3088\u3073\u65b9\u5411\u3092\u901a\u308b\u5e73\u9762\u306b\u5c5e\u3057\u307e\u3059\u3002

$$ {\\vec V_1(a,b,c)} $$<\/div> 3 \u3064\u306e\u30d9\u30af\u30c8\u30eb\u304c\u5b58\u5728\u3059\u308b\u5834\u5408\u306b\u9650\u308a\u3001\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002
$$ {\\overrightarrow{M_1M},\\overrightarrow{M_2M_1},\\vec V} $$<\/div>\u306f\u540c\u4e00\u5e73\u9762\u4e0a\u306b\u3042\u308b\u305f\u3081\u3001\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002 <\/p>
$$ { \\det(\\overrightarrow{M_1M},\\overrightarrow{M_2M_1},\\vec V)=0 } $$<\/div><\/dd><\/dl>

\u305d\u306e\u65b9\u7a0b\u5f0f\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059\u3002 <\/p>

$$ {\\begin{vmatrix} x-x_1 & x_2-x_1 & a\\\\ y-y_1 & y_2-y_1 & b\\\\ z-z_1 & z_2-z_1 & c \\end{vmatrix} = 0 } $$<\/div><\/dd><\/dl>

3 \u3064\u306e\u4f4d\u7f6e\u304c\u63c3\u3063\u3066\u3044\u306a\u3044\u70b9\u306b\u3088\u3063\u3066\u5b9a\u7fa9\u3055\u308c\u308b\u5e73\u9762<\/span><\/h4>

M<\/i> 1<\/sub> ( x<\/i> 1<\/sub> , y<\/i> 1<\/sub> , z<\/i> 1<\/sub> )\u3001 M<\/i> 2<\/sub> ( x<\/i> 2<\/sub> , y<\/i> 2<\/sub> , z<\/i> 2<\/sub> )\u3001 M<\/i> 3<\/sub> ( x<\/i> 3<\/sub> , y<\/i> 3<\/sub> , z<\/i> 3<\/sub> ) \u3068\u3044\u3046\u4f4d\u7f6e<\/span>\u5408\u308f\u305b\u3055\u308c\u3066\u3044\u306a\u3044\u70b9\u3092 3 \u3064\u3068\u3057\u307e\u3057\u3087\u3046\u3002<\/p>

\u4e0a\u8a18\u3068\u985e\u63a8\u3059\u308b\u3068\u3001\u3053\u308c\u3089 3 \u70b9\u3092\u901a\u308b\u5e73\u9762\u306e\u65b9\u7a0b\u5f0f\u306f\u6b21\u306e\u3088\u3046\u306b\u306a\u308a\u307e\u3059\u3002 <\/p>

$$ {\\begin{vmatrix} x-x_1 & x_2-x_1 & x_3-x_2\\\\ y-y_1 & y_2-y_1 & y_3-y_2\\\\ z-z_1 & z_2-z_1 & z_3-z_2 \\end{vmatrix} = 0 } $$<\/div><\/dd><\/dl><\/div>

\u53c2\u8003\u8cc7\u6599<\/h2>
  1. \u0645\u062a\u0631\u064a (\u062a\u0648\u0636\u064a\u062d) \u2013 arabe<\/a><\/li>
  2. Metrik \u2013 bavarois<\/a><\/li>
  3. Metrika \u2013 tch\u00e8que<\/a><\/li>
  4. Metrik \u2013 danois<\/a><\/li>
  5. Metrik \u2013 allemand<\/a><\/li>
  6. \u039c\u03b5\u03c4\u03c1\u03b9\u03ba\u03ae \u2013 grec<\/a><\/li><\/ol><\/div>\n
    \n

    \n \u7dda\u3068\u5e73\u9762\u306e\u30e1\u30fc\u30c8\u30eb\u7279\u6027 – \u5b9a\u7fa9\u30fb\u95a2\u9023\u52d5\u753b\n <\/h2>\n
    \n \n
    \n
    \n