作者Poplarysl (Poplar)
看板NTU-K6
標題Re: [閒聊]
時間Tue Oct 19 00:54:16 2010
一樣騙P幣
※ 引述《maxcsh (ㄚ翰)》之銘言:
※ 引述《tobe6104 (拖拖拖拖比)》之銘言:
: 空間中給A(0,0,0),B(1,1,√2),C(2,0,0)三點座標
: 如ABCD為一正四面體,求D點座標。
難得沒事來騙騙P幣好了,
設D(x,y,z),由四邊等距:
x^2 + y^2 + z^2 = (x-1)^2 + (y-1)^2 + (z-√2)^2 = (x-2)^2 + y^2 + z^2 = 4
=> 2x-1 + 2y-1 + 2√2z-2 = 0
4x-4 = 0
x^2 + y^2 + z^2 = 4
=> x = 1
=> 2y + 2√2z = 2
y^2 + z^2 = 3
=> z =
-(y - 1)/√2 代入得 3y^2 - 2y - 5 = 0
=> y = -1 or 5/3 => z = √2 or -√2/3
=> D( 1 , -1 , √2 ) or D( 1 , 5/3 ,-√2/3 )
以上沒拿筆純靠爛爛的心算,算錯概不負責=.=
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◆ From: 140.112.249.113
1F:推 tobe6104:好直接喔 那求重心在用abc平面法向量延伸四面體的高這方 10/19 00:46
2F:→ tobe6104:法爛不爛= = 10/19 00:47
3F:推 Poplarysl:其實算錯了 = = 10/19 00:48
4F:→ maxcsh:樓上幫忙補完,我懶得檢查 10/19 00:49
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※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 140.112.249.93
5F:→ Poplarysl:ㄎ 10/19 00:54
6F:推 maxcsh:水,這你也看得出來 10/19 00:56
7F:→ Poplarysl:因為跟我算的不一樣ㄎㄎ 10/19 00:56
8F:推 tobe6104:耶耶 下星期你們幫我去好了XD 10/19 01:23
9F:推 maxcsh:時薪>500的話再考慮一下= =+ 10/19 01:24
10F:→ tobe6104:我真的覺得這個必帶的服務學習很詭異= = 10/19 23:43
11F:→ tobe6104:根本是去補習班... 10/19 23:43
12F:推 yuuirain:這是服務學習喔?! 10/20 13:02
13F:→ tobe6104:嗯去了才知道= = 10/20 16:01