Finding unit Tangent Vector, Unit Normal vector, and Binormal Vector

[Drum_2014]

I have the equation r(t)=<e^t cost, e^t sint, e^t> and i have to find the unit Tangent Vector, unit normal vector, and the unity binormal vector for the equation.

I have gotten so far that the r'(t)=<e^t cost- e^t sint, e^tsint- e^t cost,e^t> and I dont know what to do next

I NEED HELP!!!!!

 

[HallsofIvy]

I have the equation r(t)=<e^t cost, e^t sint, e^t> and i have to find the unit Tangent Vector, unit normal vector, and the unity binormal vector for the equation.

I have gotten so far that the r'(t)=<e^t cost- e^t sint, e^tsint- e^t cost,e^t>

The middle term is incorrect. The derivative of sin t is cos t, not -cos t.

and I dont know what to do next

I NEED HELP!!!!!

r'(t) points in the direction of the tangent so now you need to divide by its length.
Differentiate THAT to get a normal vector, find its length and divide it by its length to get the unit normal vector. Finally, take the cross product of the unit tangent vector and unit normal vector to get the unit binormal vector.