Unit Tangent Vectors for Position Vectors: Finding T(t) for Given Values of t

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Homework Help Overview

The discussion revolves around finding unit tangent vectors T(t) for various position vectors r(t) at specified values of t. The subject area includes vector calculus and the concept of derivatives in relation to tangent vectors.

Discussion Character

  • Exploratory, Mathematical reasoning, Problem interpretation

Approaches and Questions Raised

  • Participants discuss the process of finding the unit tangent vector by taking the derivative of the position vector and dividing by its magnitude. There are questions about the correctness of their calculations and the results obtained from a computer.

Discussion Status

Some participants have shared their computed results and expressed confusion over discrepancies with expected answers. There is an ongoing exploration of the steps taken to derive the unit tangent vectors, with requests for clarification and sharing of specific calculations.

Contextual Notes

Participants are working under the constraints of homework rules, which may limit the information they can share or the methods they can use. There is an indication of frustration with the accuracy of their results as verified by a computer system.

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positon vectors r(t) find the unit tangent vectors T(t) for the given value of t

r(t) = (cos5t, sin5t)
T(pi/4) = ( , )

r(t) = (t^2, t^3)
T(1) = ?

r(t) = e^5t i + e^-1t j + t k
T(2) = ? i+ ? j+ ? k

now the to find it i use r'(t)/lr'(t)l
I did that, but i get wrong answers i don't know what I am doing wrong because all i c is that is how u find the unit tangent vectors... someone please help me and explain what u did.. thanks a lot!
 
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the derivative is the tangent vector.
then divide it by its magnitude to get unit tangent vector.
 
I did that and the damn computer say i got the wrong answers... like the 1st one i took it derivative then i divid it by its magnitude which is squaring everything and sq rt it right that's what i did..
 
give the answer that you have found for the first one.
 
well i worked out the second one i got (1, 1) i really I am doing something stupid
 
i get 2/sq rt of 13, 3/ sq rt of 13
what is wrong with your steps?
 

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