For the given position vectors rt compute the unit tangent v

For the given position vectors r(t) compute the unit tangent vector T(t) for the given value of t

Solution

r\' = 5e^5ti - 4e^-4tj + 1k

Ir\'I= (25e^10t + 16e^-8t + 1)

T(t) = 5e^5ti/ (25e^10t + 16e^-8t + 1) - 4e^-4tj/ (25e^10t + 16e^-8t + 1) + 1k/ (25e^10t + 16e^-8t + 1)

T(-4) = 5e^-20i/(25e^-40 + 16e³² + 1) - 4e¹⁶j/(25e^-40 + 16e³² + 1) + 1k/(25e^-40 + 16e³² + 1)