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

  1. Oct 30, 2016 #1
    1. The problem statement, all variables and given/known data
    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

    2. Relevant equations


    3. 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)
     

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  3. Oct 30, 2016 #2

    PeroK

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    Science Advisor
    Homework Helper
    Gold Member

    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.
     
  4. Oct 30, 2016 #3
    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 ?
     
  5. Oct 30, 2016 #4

    Mark44

    Staff: Mentor

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