multi-variable calculus

神龍劍士

小弟係美國讀緊1yr college
呢2題係美國multi-variable calculus既extra credit problem
唔該各位高人幫幫忙 堅唔識做
show steps 麻煩哂

1. Let u,v and w be three vectors such that v and w are orthogonal and have the same length r, and let c(t) = u + (cost)v + (sint)w . Describe the motion of the tip of c(t) if the tail of c(t) is fixed at the origin. (That is, describe the parametric curve corresponding to c(t) .)

2.
圖link -->
It desired to carry a long thin rod down a corridor [ b ] feet wide and around a square corner into another corridor [ a ] feet wide. What is the longest rod with which this can be managed if the rod is kept horizontal and is never bent?

括住果2個係variable黎

Naozumi

1.
c(t) = u + (cost)v + (sint)w
c(t) - u = (cost)v + (sint)w
|c(t) - u|^2 = |(cost)v + (sint)w|^2
                  = [(cost)v + (sint)w] [(cost)v + (sint)w]
                  = (cos^2 t) |v|^2 + 2(vw)sint cost  + (sin^2 t) |w|^2
                  = r^2 (cos^2 t) + 2(0)sint cost  + r^2 (sin^2 t)
                  = r^2
So it is the circle with centred at u and radius r

神龍劍士

原帖由 Naozumi 於 2009-4-7 01:49 PM 發表
1.
c(t) = u + (cost)v + (sint)w
c(t) - u = (cost)v + (sint)w
|c(t) - u|^2 = |(cost)v + (sint)w|^2
                  = [(cost)v + (sint)w] [(cost)v + (sint)w]
                  = (cos^2 t) |v|^2 + ...

神人@@ XXXX果d人答到好9唔答8咁~_~
希望大佬可以幫埋我第2題><

Naozumi: 不好意思,因為不想引起其他網站的朋友反感,請不要"點名"評論

[ 本帖最後由 Naozumi 於 2009-4-7 08:13 PM 編輯 ]

Naozumi

你另一題要畫圖,等我吃埋晚飯再攪

神龍劍士

原帖由 Naozumi 於 2009-4-7 08:13 PM 發表
你另一題要畫圖,等我吃埋晚飯再攪

ok 麻煩哂大佬
題目我都唔多明~.~

Naozumi

剩番d手尾,例如: 要check maximum point, 個total length留番樓主慢慢攪

[ 本帖最後由 Naozumi 於 2009-4-7 09:54 PM 編輯 ]