Unit tangent vector of r(t) = (e^t)(cos t ) i + (e^t)(sin t

[chetzread]

Homework Statement

Find the unit tangent vector T(t) for vector valued function r(t) = (e^t)(cos t ) i + (e^t)(sin t ) j + (e^t) k

Homework Equations

The Attempt at a Solution

i gt stucked here ...
, the ans is [1/ sqrt (3) ] [ (cos t -sin t ) i + (sin t + cos t ) j +k) [/B]

 

[PeroK]

Homework Statement

Find the unit tangent vector T(t) for vector valued function r(t) = (e^t)(cos t ) i + (e^t)(sin t ) j + (e^t) k

Homework Equations

The Attempt at a Solution

i gt stucked here ...
, the ans is [1/ sqrt (3) ] [ (cos t -sin t ) i + (sin t + cos t ) j +k) [/B]

You got $r'(t)$ okay, but you didn't calculate its magnitude correctly. I would factor out the $e^t$ term first. Then you need to take more care with your algebra.

 

[chetzread]

You got $r'(t)$ okay, but you didn't calculate its magnitude correctly. I would factor out the $e^t$ term first. Then you need to take more care with your algebra.

My ans is [1/ sqrt (2) ] [ (cos t -sin t ) i + (sin t + cos t ) j +k)
But not
[1/ sqrt (3) ] [ (cos t -sin t ) i + (sin t + cos t )
j +k)

Is the given ans wrong ?

 

[Mark44]

My ans is [1/ sqrt (2) ] [ (cos t -sin t ) i + (sin t + cos t ) j +k)
But not
[1/ sqrt (3) ] [ (cos t -sin t ) i + (sin t + cos t )
j +k)

Is the given ans wrong ?

No, your answer is wrong. I get the same answer that you showed in post #1.
Please show your work for |r'(t)|.