r[u_] := {3 Cos[u] + 2 Sin[u], -2 Cos[u] Sin[2 u], u}; tanv[u_] := D[r[u], u]/Sqrt[D[r[u], u].D[r[u], u]]; norv[u_] := D[tanv[u], u]/Sqrt[D[tanv[u], u].D[tanv[u], u]]; binv[u_] := Cross[tanv[u], norv[u]]; scale = 3; tang[t_] = Graphics3D[{RGBColor[0, 1, 0], Arrow[{r[t], r[t] + scale tanv[u] /. u -> t}]}]; norm[t_] = Graphics3D[{RGBColor[0, 0, 1], Arrow[{r[t], r[t] + scale norv[u] /. u -> t}]}]; binorm[t_] = Graphics3D[{RGBColor[1, 0, 0], Arrow[{r[t], r[t] + scale binv[u] /. u -> t}]}]; Manipulate[ Grid[{{Column[{ Labeled[Framed[Round[tanv[u] /. u -> t, 0.01]], Style[ "Unit Tangent", Darker[Green], Bold], Top], Labeled[Framed[Round[norv[u] /. u -> t, 0.01]], Style[ "Unit Normal", Blue, Bold], Top], Labeled[Framed[Round[binv[u] /. u -> t, 0.01]], Style[ "Binormal", Red, Bold], Top]}, Center]}}] Show[ParametricPlot3D[r[t], {t, 0, 2 \[Pi] }, AxesLabel -> {x, y, z}, PlotRange -> {{-5, 5}, {-5, 5}, {-4, 8}}, ImageSize -> {440, 370}], tang[t], norm[t], binorm[t]], {{t, 0.2}, 0, 2 \[Pi] }]