write the position vector and
升研究所的數學問題 (工程數學) 難!!
(a)write the position vector and tangent vector for the curve whose parametric equations are given
(b)find a length function s(t) for the curve
(c)write the position vector as a function of s
(d)verify that the resulting position vector has a derivative of length 1.
( 1 =< t =< 3 )
- mathmanliuLv 71 decade agoFavorite Answer
(a)Position vector r(t)=(2t2, 3t2, 4t2) , 1<=t<=3
Tangent vector T(t)=(4t, 6t, 8t)
(b) s(t)=∫1t |T(x)| dx=√29(t2-1)
(c) t2=s/√29 +1
=> Position r(s)=(2+2s/√29, 3+3s/√29, 4+4s/√29)
(d) T(s)=dr/ds=(2/√29, 3/√29, 4/√29)