I am not sure what you want to do. Keep in mind that matrix multiplication is done with . and not with *

This is my interpretation of your wish:

f0[t_] = {x[t, 1, 2], y[t, 1, 2], z[t, 1, 2]};
f1[t_] = {x2[t_], y2[t_], z2[t_]} =
   f0[t] +
    T1[t] x[2 t, 1, 2] +
    N1[t] y[2 t, 1, 2] +
    B1[t] z[2 t, 1, 2];
curves = 
  ParametricPlot3D[{f0[t], f1[t]}, {t, -4 Pi, 4 Pi}, PlotRange -> All]
Manipulate[
 Show[curves, Graphics3D[{{PointSize[Large], Blue, Point[f0[t]],
     Brown, Point[f1[t]]}, HalfLine[f0[t], T1[t]],
    Arrow[{f0[t], f0[t] + 15 T1[t]}], HalfLine[f0[t], N1[t]],
    Arrow[{f0[t], f0[t] + 15 N1[t]}], HalfLine[f0[t], B1[t]],
    Arrow[{f0[t], f0[t] + 15 B1[t]}]}]],
 {t, -4 Pi, 4 Pi}]

Try with

f1[t_] = {x2[t_], y2[t_], z2[t_]} = f0[t] +
    N1[t] Cos[2 t] + B1[t] Sin[2 t];