[Razor]

We are currently working with vectors at school on our math classes but these are vectors in 3d so they all have x y z coordinates. Is there a progie that can enable me to see clearly all the stuff I draw in 3D( lines, objects, direction vectors etc...). It is very confusing when this is done on a piece of paper or on a calculator (which are of course 2d).

[kode]

I only ever used the drawing for show, anyways. the real picture must be in your head... try using support lines, also.

[Stealth]

let me guess:  Pre-Calculus?

i did that a while back, but i never needed to do it another way.  i t was hard to understand, but it was possible to do it without using anything but your head

[Ashrak]

your head is the most powerful computer on this planet so use it think 3d i think 4 d

[CP5670]

Do you just need to do vectors? Let me guess, linear algebra? You usually don't need to visualize those to do anything with them though, especially since the vectors commonly come up in arbitrary n dimensions. If you really need to do it though, you could probably just create a line in a 3D modeling program with the appropriate endpoint coordinates.

Or do you mean 3D vector fields? I know of a program that does those as well as 3D equation graphs very well, but it isn't free. Or if you happen to have one of the major math programming packages (e.g. Mathematica, Maple and so on), those can do it too.

[Stealth]

you're just going to confuse him even more CP

[Galemp]

Why not use waypoints in FRED? You plop one down then plug in the x, y, and z coordinates.

[Petrarch of the VBB]

I've been known to do that before. I have also used POVRAY for that purpose, and to make a cube with all it's corners on the inside.

[Falcon X]

For symbolic and such Mathematica is the best... but at a pretty penny.  Search Kazaa for it.

Also, in Calc3 we never really had to worry about what they looked like.  just get a feel for them.  You won't have a program in the test.

[Razor]

Originally posted by CP5670
Do you just need to do vectors? Let me guess, linear algebra? You usually don't need to visualize those to do anything with them though, especially since the vectors commonly come up in arbitrary n dimensions. If you really need to do it though, you could probably just create a line in a 3D modeling program with the appropriate endpoint coordinates.

Or do you mean 3D vector fields? I know of a program that does those as well as 3D equation graphs very well, but it isn't free. Or if you happen to have one of the major math programming packages (e.g. Mathematica, Maple and so on), those can do it too.

you're just going to confuse him even more CP  

First, he is not confusing me. I (think I) know exactly what he is talking about.

It may be linear algebra. The chapter name is: Curves and vector functions. There is also something called: "Polar" coordinates and about finding something called: cartesis (sp) coordinates. Some guy called: Rene Descartes invented those. But what is really confusing to me is something called: areas and polar coordinates. It is something about calculating areal coverage of a graph (which is usually a curve line or a spiral created with a particular function) by using Integral functions. By the way, this is funny stuff. Some of those lines can look like flowers or something.
There is also something about parameters and stuff. By the way CP, do you have any clue what I am talking about? It's tough to translate stuff from Norwegian to English.

WARNING!!! THIS WAS NOT SPAM!

[beatspete]

Don't think, just add the numbers in the brackets.

[Razor]

What does that have to do with vectors in 3d?
Oh I know. You dont have a clue what I am talking about.

[beatspete]

(0)
|3|   (but with 2 big brackets)
(1)
...would be a vector.  Add/subtract to other vectors (in brackets) to get new resultant vectors.
Been a while since i did them, i'll shut up now.

[wojta]

Useful for learning linear algebra:

 http://www.matrixanalysis.com/

you can download here whole textbook

[CP5670]

It may be linear algebra. The chapter name is: Curves and vector functions. There is also something called: "Polar" coordinates and about finding something called: cartesis (sp) coordinates. Some guy called: Rene Descartes invented those. But what is really confusing to me is something called: areas and polar coordinates. It is something about calculating areal coverage of a graph (which is usually a curve line or a spiral created with a particular function) by using Integral functions. By the way, this is funny stuff. Some of those lines can look like flowers or something.
There is also something about parameters and stuff. By the way CP, do you have any clue what I am talking about? It's tough to translate stuff from Norwegian to English.

Oh I think I see what you mean now; you want to plot vector-valued functions. However, from what you are saying here it looks like you only need to plot 2D rectangular and polar functions, so you shouldn't really have to worry about 3D here. This sounds like the material in a first year calculus course if I remember correctly, where they don't do any 3D stuff aside from possibly quadratic surfaces. Anyway, you can graph the stuff you encounter there on a graphing calculator, although it tends to be somewhat slow and you cannot plot implicit functions at all.

You might want to try GrafEq; this is about the best free 2D graphing program if you don't need to use special functions, as it is fairly fast and particularly excels at graphing implicit relations. Although it is shareware, the trial version is fully functional aside from a popup message at startup. This program cannot do 3D though.

As for the flowers, you haven't seen anything yet; some of the graphs can get extremely weird...

For symbolic and such Mathematica is the best... but at a pretty penny. Search Kazaa for it.

That's what I use for all my stuff; an awesome program. It seems to be nearly impossible to find this on the internet, but at least I was able to get the much more affordable student edition.

[Razor]

Well there is actually some 3d stuff. Like calculating the volumes of 3d objects ( but I know that) and distances between points and plains and all that crap. But I think integration is the weirdest.

Like listen to this example:

You have a line "l" going through a point A (1, 0, -2) and a way vector: r [4, 3, 3]. Find the coordinates to the two points on the line "l" which have a distance 3 from the point (7, 4, 3).

This is just to show you that there is 3d here.

[CP5670]

hmm, actually they do sometimes merge parts of normal calculus and parts of vector calculus into one class, so you might be doing one of those courses since it looks like you have both integrals and vector computations. Anyway, for just drawing individual vectors like that, you should be able to do it quite easily in something like 3DS max (or even FRED2, as GE said ) by just drawing lines with the appropriate endpoints. It gets more complicated when you want a whole series of points/vectors defined by functions, since then the program needs both a graphics component and a numerical computation component (this is the part that most normal 3D programs do not have) to generate a graph.

[Top Gun]

Originally posted by Razor




First, he is not confusing me. I (think I) know exactly what he is talking about.

It may be linear algebra. The chapter name is: Curves and vector functions. There is also something called: "Polar" coordinates and about finding something called: cartesis (sp) coordinates. Some guy called: Rene Descartes invented those. But what is really confusing to me is something called: areas and polar coordinates. It is something about calculating areal coverage of a graph (which is usually a curve line or a spiral created with a particular function) by using Integral functions. By the way, this is funny stuff. Some of those lines can look like flowers or something.
There is also something about parameters and stuff. By the way CP, do you have any clue what I am talking about? It's tough to translate stuff from Norwegian to English.

Cartesian Co-ordinates are the ones you are used to (three values from a given point in the x, y and z directions), Polar co-ordinates (in 2D anyways) is where you have an angle from a line and a direction from a pole (hence the name), there are also parametric co-ordinates. I think the course wants you to be able to find the cartesian equation (thing you're used to finging ie. x=y=z) from vector equations.




Here's some formulas for areas 3D shapes


|axb|.c = for a parallelapiped (sp?)
1/6 |axb|.c = for a tetrahedron
|a|^3 = for a cube
1/2|axb|*c = for a triangular prisim
|a|*|b|*|c| = for a cuboid

a, b and c are the vectors which make up your shape

a= (a1,a2,a3) b = (b1,b2,b3) c = (c1,c2,c3)

* means multiply

|| means the lenglth of the vector (use pythagaros for single ones)

x means the vector product. It can be found by putting your vectors a and b into the 2nd and third row of a 3by3 matrix and then finding the determinant. eg ([x,y,z],[a1,a2,a3],[b1,b2,b3]). If you don't know how do do that then find out, the alternative method is bloody long.

. is the scalar product, multiply each dimention together then add them up eg a.b = (a1*b1)+(a2*b2)+(a3*b3)

I doubt you'll be given curves in vector form so you should be OK.

[Razor]

Originally posted by Top Gun


Cartesian Co-ordinates are the ones you are used to (three values from a given point in the x, y and z directions), Polar co-ordinates (in 2D anyways) is where you have an angle from a line and a direction from a pole (hence the name), there are also parametric co-ordinates. I think the course wants you to be able to find the cartesian equation (thing you're used to finging ie. x=y=z) from vector equations.




Here's some formulas for areas 3D shapes


|axb|.c = for a parallelapiped (sp?)
1/6 |axb|.c = for a tetrahedron
|a|^3 = for a cube
1/2|axb|*c = for a triangular prisim
|a|*|b|*|c| = for a cuboid

a, b and c are the vectors which make up your shape

a= (a1,a2,a3) b = (b1,b2,b3) c = (c1,c2,c3)

* means multiply

|| means the lenglth of the vector (use pythagaros for single ones)

x means the vector product. It can be found by putting your vectors a and b into the 2nd and third row of a 3by3 matrix and then finding the determinant. eg ([x,y,z],[a1,a2,a3],[b1,b2,b3]). If you don't know how do do that then find out, the alternative method is bloody long.

. is the scalar product, multiply each dimention together then add them up eg a.b = (a1*b1)+(a2*b2)+(a3*b3)

I doubt you'll be given curves in vector form so you should be OK.

Thanks for the tips Top Gun. I allready know some of that stuff, but some those things you wrote there might come in handy later on.

[Falcon X]

I always prefered the i j k format.