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Homework Help: Vector valued functions: finding tangent line

  1. Sep 26, 2012 #1
    1. The problem statement, all variables and given/known data
    Find the unit tangent vector T(t) and find a set of parametric equations for the line tangent to the space curve at point P

    r(t)= <2sin(t), 2cos(t), 4sin2(t)>, P(1, √3, 1)

    3. The attempt at a solution
    I found T(t) using the formula T(t)= r'(t)/||r'(t)||

    r'(t)= <2cos(t), -2sin(t), 8sin(t)cos(t)>

    ∴ T(t)= <2cos(t), -2sin(t), 8sin(t)cos(t)>/ 2+8sin(t)cos(t)
    -note: i could do more to the denominator as far as trig functions and algebra but i dont know if it is useful.

    What i don't understand is how the point is used to find the parametric equation.
  2. jcsd
  3. Sep 26, 2012 #2


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    Staff Emeritus
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    You have left out the square root for ||r' ||, as well as there is another error as noted above.

    Do you know the general form of a parametric equation of a line in vector form?
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