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Homework Help: Find parametric equations for the tangent line

  1. Sep 8, 2014 #1
    1. The problem statement, all variables and given/known data

    Find parametric equations for the tangent line to the curve with the given parametric equations at the specified point.

    2. Relevant equations

    [tex] x = 1+2 \sqrt{t}, \quad y = t^3 - t, \quad z = t^3 + t, \quad (3, 0, 2) [/tex]

    3. The attempt at a solution

    I began by re-writing this as [tex] \vec{r}(t) = <1+2 \sqrt{t}, \quad t^3 - t, \quad t^3 + t > [/tex]
    and then taking the derivative to find the normal vector: [tex] \vec{r}(t) = <1/ \sqrt{t}, \quad 3t^2 - 1, \quad 3t^2 + 1> [/tex]. From here, I tried plugging in (3, 0, 2) into each of the components for the derivative, but that hasn't worked. I think I need to find a value to use for "t" and then put that into the normal vector, but I am not sure how.
  2. jcsd
  3. Sep 8, 2014 #2


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    Part of your problem may be you are calling both the original equation and its derivative ##r(t)##. Find the ##t## that makes the original equation pass through ##(3,0,2)##.
  4. Sep 8, 2014 #3

    Ray Vickson

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    Please distinguish between ##\vec{r}(t)## and ##\vec{r}'(t)##, which is your second one. Anyway ##\vec{r}'(t)## is NOT a "normal vector"! Can you describe what it actually IS?
  5. Sep 8, 2014 #4
    I made a mistake. I meant to say tangent vector.
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