How do I write and manipulate a vector equation in Mathematica?

[flyingpig]

Homework Statement

Alright I searched all over Mathematica on Google and I can't find the answer.

How do you write out a vector equation and then do a bunch fancy stuff to it? (Like if it was a parametric surface or line, how do you graph it? Find the derivative? Integrate it?)

For instance, I want to graph the parametric surface

$$r(\theta, \phi) = <2cos\theta sin\phi,2sin\theta sin\phi, 2cos\phi>$$

How do I do this? Also how do I take the partial derivative of this parametric equation on Mathematica?

The Attempt at a Solution

I don't have a clue...

 

[KataKoniK]

Thank you for your question. I understand the frustration of not being able to find the answer to a problem. However, in order to effectively help you, I would need more information on what you have tried so far and what specific issues you are facing. In general, to write a vector equation in Mathematica, you can use the "Vector" command, followed by the components of the vector enclosed in curly brackets. For example, the vector equation r(\theta, \phi) = <2cos\theta sin\phi,2sin\theta sin\phi, 2cos\phi> can be written as "r[\[Theta],\[Phi]] = {2Cos[\[Theta]]Sin[\[Phi]],2Sin[\[Theta]]Sin[\[Phi]],2Cos[\[Phi]]}".

To graph this parametric surface, you can use the "ParametricPlot3D" command, specifying the range for \[Theta] and \[Phi]. For example, "ParametricPlot3D[{2Cos[\[Theta]]Sin[\[Phi]],2Sin[\[Theta]]Sin[\[Phi]],2Cos[\[Phi]]}, {\[Theta], 0, 2\[Pi]}, {\[Phi], 0, \[Pi]}]" will plot the surface for values of \[Theta] ranging from 0 to 2\[Pi] and \[Phi] ranging from 0 to \[Pi].

To find the derivative of this parametric equation, you can use the "D" command followed by the parameters and variables you want to differentiate with respect to. For example, "D[r[\[Theta],\[Phi]],\[Theta]]" will give you the partial derivative of r with respect to \[Theta].

I hope this helps. If you are still having trouble, please provide more information and I will be happy to assist further. Good luck with your problem!


(Scientist)