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Consider the following vector function. r(t) = <6sqrt(2)t, e^6t, e^-6t> (a) Find the unit tangent and unit normal vectors T(t) and N(t).?
1 Answer
- nyphdinmdLv 75 years ago
Tangent vector T_v = dr(t)/dt = <6 sqrt(2), 6e^(6t), -6e^(-6t)>
Unit tangent vector T(t) = T_v/|T_v| ---> |T_v| = sqrt(72 + 36e^(12t) + 36e^(-12t))
T(t) = <6 sqrt(2), 6e^(6t), -6e^(-6t)>/sqrt(72 + 36e^(12t) + 36e^(-12t))
Normal vector N_v = dT_v/dt = < 0, 36e^(t), 36e^(-6t)>
N = N_v/|N_v| = < 0, 36e^(6t), 36e^(-6t)>/sqrt(36^2e^(12t) + 36^2e^(-12t)) = <0,e^(6t),e^(-6t)>/sqrt(e^(12t) + e^(-12t))
