haha
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haha asked in 科學數學 · 1 decade ago

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.

x=2(t^2)

y=3(t^2)

z=4(t^2)

( 1 =< t =< 3 )

1 Answer

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  • 1 decade ago
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    (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)

    =>|dr/ds|=1

    註:粗體字為向量

    Source(s): me
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