# Application of individual vectors in parametric diagrams I'm trying to draw something like the Frenet-Serret formulas with a parametric plot:

``````    r[t_] := {t, t^2, 2 t^3/3}
t[t_] := r'
Manipulate[ParametricPlot3D[{r
PlotRange -> {{-0.1, 1.1}, {-0.1, 1.1}, {-0.1, 1.1}}], {p, 10^-10, 1}]
``````

Now I want to have the function `t[x]` also drawn, but as a single vector at the coordinates of the current point `r[p]`,

This probably helps to visualize what I am trying, since it is exactly the same: frenet-serret frame moving along a parametric helix

The helix would be my function `r` and `t` is the first of these three vectors that I would like to see moved.

I tried two things, first with

``````Manipulate[ParametricPlot3D[{r
PlotRange -> {{-0.1, 1.1}, {-0.1, 1.1}, {-0.1, 1.1}},
Epilog -> {Arrow[{r[p], t[p]}]}], {p, 10^-10, 1}]
``````

However, the arrow will be displayed as a 2D overlay above the plot

``````Manipulate[ParametricPlot3D[{r
PlotRange -> {{-0.1, 1.1}, {-0.1, 1.1}, {-0.1, 1.1}},
Epilog -> {ParametricPlot3D[t[p]*u, {u, 0, 1}] /. Line -> Arrow}], {p, 10^-10, 1}]
``````

what I can not get to work there `ParametricPlot3D` is not a primitive in which to show `Epilog`

So any ideas? I'm sure because I'm just a noob.

Thanks in advance guys and have a nice day :] Posted on Categories Articles