Plotting Vector and Derivative: A Frustrating Challenge

AI Thread Summary
The discussion focuses on the challenges of plotting a vector and its derivative in a 3D space using Mathematica. The user provides their code, which attempts to create parametric plots for both the vector and its derivative but encounters issues. Suggestions include first successfully plotting the vector V[t] over the desired range and then plotting the derivative separately at the specific point Pi/4. It is emphasized that the derivative should not be plotted over the same range as the vector. Finally, guidance is given to combine the two plots using specific methods from the Wolfram documentation.
dpeagler
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I have been trying to plot a vector and it's derivative for a while now, but I cannot figure out why I can't get them to plot.

Here is what I put for my code...

a[t_] := Sin[t] Cos[2 t]
b[t_] := Sin[t] Sin[2 t]
c[t_] := Cos[t]
V[t_] := {a, b, c}

I tried this...

ParametricPlot[{a[t], b[t], c[t]}, {a'[t], b'[t], c'[t]}, {t, -\[Pi]/2, \[Pi]/2}, {t, \[Pi]/4}]

and this...

ParametricPlot[{V[t]},{V'[\[Pi]/4]},{{t, -\[Pi]/2, \[Pi]/2}

The function is seen as V[t]. I want to graph it from -Pi/2 to Pi/2 and I want to have V'[Pi/4] on the same graph. And then I want to have two different images.

I know that's a lot, but I'm sure it's something really simple that I'm missing. Thanks to anyone who can give any advice.
 
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See if you can just plot the vector first.

a[t_] := Sin[t] Cos[2 t];
b[t_] := Sin[t] Sin[2 t];
c[t_] := Cos[t];
V[t_] := {a[t], b[t], c[t]};
ParametricPlot3D[V[t], {t, -Pi/2, Pi/2}]

If that works then compare what I did with what you did and figure out the differences.

After that see if you can just plot the derivative

ParametricPlot3D[{a'[t], b'[t], c'[t]}, {t, -Pi/2, Pi/2}]

After that perhaps you can start thinking about combining the two
 
Thanks for the response. The only thing I am confused about is why you are plotting the derivative over the same range. It is only supposed to be at the point Pi/4
 

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