求空间曲线x=e^t,y=t^2,z=t^3在点M(e,1,1)处的切线和法如

Question

求空间曲线x=e^t,y=t^2,z=t^3在点M(e,1,1)处的切线和法
如

Answer 1

x'=e^t,y'=2t,z'=3t^2,
t=1时x'=e,y'=2,z'=3,
空间曲线x=e^t,y=t^2,z=t^3在点M(e,1,1)处的切线方程是
(x-e)/e=(y-1)/2=(z-1)/3.