Find the tangent vector and the arc length of the indicated portion of the curve.

r(t) = e^tcos ti + e^t sin tj+e^tk for -ln4

Question

Find the tangent vector and the arc length of the indicated portion of the curve.

r(t) = e^tcos ti + e^t sin tj+e^tk for -ln4 <= t <= 0.

Any Help is warmly appreciated 

Kind regards

turingtest · Answer

the tangent vector is just the derivative of the position vector with respect to time
just take the derivative f each component

anonymous · Answer

Hi Turing...nice to see you here. You were a great help last time. I managed to pass my maths and am now in 2nd year engineering.

anonymous · Answer

what about the arc length?
Is the arc length the magnitude , I think?

turingtest · Answer

I'm so glad to hear that, congratulations!!!
I am honored that you feel I was of some help :D

turingtest · Answer

and you are exactly right, arc length is the magnitude of that parametric tangent function integrated along the given bounds for t

turingtest · Answer

so$$L=\int_a^b\|\vec r'(t)\|dt$$

turingtest · Answer

...where $a\le t\le b$

anonymous · Answer

Okay ...thanks for your help. You've been great again and once again I'm off to a good start!

turingtest · Answer

nice!