[工數] 非常誠心請教怎麼計算

看板Math作者 (影)時間10年前 (2014/03/25 13:33), 編輯推噓0(0012)
留言12則, 4人參與, 4年前最新討論串1/1
小弟工數神爛 所以請想問板上的神人大大們...怎麼計算這幾題 Suppose r(t) is a differentiable vector function for which r(t) = c for all t. Show that r'(t) is perpendicular to r(t) for all t. 還有這題.. r(t) = (3cos t)i + (3sin t)j + (t/4)k , t ≧0 , is the position vector of a moving particle. Find the velocity, speed, acceleration, unit tangent vector, unit normal vector and curvature. 非常謝謝大大們 -- ※ 發信站: 批踢踢實業坊(ptt.cc), 來自: 140.138.176.43

03/25 13:48, , 1F
第一題條件應該是|r(t)|=c吧
03/25 13:48, 1F

03/25 13:50, , 2F
r(t)·r(t)=c^2 => r'(t)·r(t)+r(t)·r'(t)=0
03/25 13:50, 2F

03/25 13:51, , 3F
得r'(t)·r(t)=0 ,r'(t)與r(t)垂直
03/25 13:51, 3F

03/25 13:53, , 4F
對~是│r(t)│=C沒錯~謝修正
03/25 13:53, 4F

03/25 13:54, , 5F
第2題照名詞的定義做就有答案...完全不用思考,請翻書
03/25 13:54, 5F

03/25 13:56, , 6F
定義不太懂...小弟之的很笨..
03/25 13:56, 6F

03/25 14:00, , 7F
en.wikipedia.org/wiki/Vector-valued_function
03/25 14:00, 7F

03/25 14:01, , 8F
裡面Derivative of a three-dimensional vector...
03/25 14:01, 8F

03/25 14:02, , 9F
照著做答案就有 定義之類的東西翻書或google比問人快
03/25 14:02, 9F

03/25 15:49, , 10F
好 了解了 非常謝謝ke大大^^"
03/25 15:49, 10F

01/02 15:43, 5年前 , 11F
r(t)r(t)=c^ http://yofuk.com
01/02 15:43, 11F

07/07 11:59, 4年前 , 12F
//yofuk.com https://noxiv.com
07/07 11:59, 12F
文章代碼(AID): #1JCHKPXv (Math)