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I define the vector function $\vec{r}(t)$ by

r[t_] = {t, Cos[t], Sin[t]}

The command r'[t] gives the vector tangent to the curve drawn by $r(t)$ for any specified value of $t$.

I can generate the curve for $r(t)$ on the interval $[0, 2\pi]$ via

ParametricPlot3D[{t, Cos[t], Sin[t]}, {t, 0, 2 Pi}]

What I would like to do is draw a tangent vector whose tail actually touches the curve. For example, I would like to draw the vector described by $r^\prime(0)$ with its tail at $r(0)$. Even better would be to wrap this inside Manipulate and draw the tangent vector for any $t \in [0, 2\pi]$. How can I accomplish either of these goals?

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    $\begingroup$ This is closely related or a duplicate of Finding unit tangent, normal, and binormal vectors for a given r(t). For the actual answer look here $\endgroup$
    – Artes
    Commented Aug 27, 2013 at 23:48
  • $\begingroup$ Typing "vector tangent" to the search engine shows many references which may help you. You should have done this first to avoid waste of your time spent on proper formatting (+1) :). $\endgroup$
    – Kuba
    Commented Aug 27, 2013 at 23:53
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    $\begingroup$ They say duplicates shouldn't be deleted (look e.g. here What are the guidelines for voting to delete questions?). You could provide an answer to your question, so that should be helpful anyway. $\endgroup$
    – Artes
    Commented Aug 28, 2013 at 0:13

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