Plotting Vector and Derivative: A Frustrating Challenge

[dpeagler]

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.

 

[Bill Simpson]

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

 

[dpeagler]

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

 

[Bill Simpson]

See if you can use the methods described here

http://reference.wolfram.com/mathematica/howto/CombineTwoOrMoreGraphics.html

to combine your parametric plot of V[t] with a point in 3D at V'[Pi/4]