BF2S Forums Mathamagicians: What the hell is a cross product?

nukchebi0 wrote:

Basically, its a process you know how to do, but have absolutely no idea how it works?

Well...yeah. I mean doing it is easy, only a few steps and easy enough to remember...

But with math I really hate memorizing rules, or just following steps...Pretty much everything I have learned in all the math classes I have taken I learned the theory real well, and could never remember steps...So I just re-derive, or I remember things looking at the situation and making sense of it.

Well I am done with math classes now, but I still don't get what exactly it IS if that makes sense....

I mean, I know the cross product of a force and the perpendicular distance to it is its moment, and that the cross product of two vectors divided by its magnitude is the normal vector, all that...I can use it fine and I get in some applications what it equates too...


But purely in the sense of Vector A and Vector B, and their relation to the cross product I don't understand...its just random steps to me and I want to know WHY.


To make it easier for who ever may be explaining it my math background goes up to diff eq/linear algebra...


Could someone with a good understanding of them at least ramble on for a bit?

Last edited by VicktorVauhn (2008-05-13 22:20:22)

VicktorVauhn wrote:

I mean, I know the cross product of a force and the perpendicular distance to it is its moment, and that the cross product of two vectors divided by its magnitude is the normal vector, all that...I can use it fine and I get in some applications what it equates too...


But purely in the sense of Vector A and Vector B, and their relation to the cross product I don't understand...its just random steps to me and I want to know WHY.

Thanks for trying though :\

But why is the cross product the correct way to find this? Why isn't it the first vector times 6 plus half the second vector (not that particular forumal, but any formula)

I guess I am looking for some kind of proof...Even if its in plain english just logic-ing (its a word, swear) through it.

Last edited by VicktorVauhn (2008-05-13 23:48:12)

max wrote:

something that has nothing to do with PCs. GTFOoftechplsthx

It has a lot to do with Pc's. When I programmed my own Computer graphics renderer I had to use it. The reason was that you had to calculate the cross product to know weather you had to "color" the triangle in the mesh cause it was "facing to you" or not had to color it cause it was facing away.

Example: if you color a dinosaur, you only want his skin on the outside to be colored. So you calculate the cross product and look if it's facing the camera or not. Also I think the light reflection had to do with it, but would have to look that up.

Another example is indeed magnetics.

To give a meaningful "geometry" explanation, it's like the Normal vector (unit vector?) so it's perpendicular on the area the two vectors make. The big difference is that the strength of the vector (and the direction) depends on the two vector's you're calculating it with.

It's not an easy concept, but there are more hard to understand concepts in maths (-1 = i² for example)

VicktorVauhn wrote:

VicktorVauhn wrote:

I mean, I know the cross product of a force and the perpendicular distance to it is its moment, and that the cross product of two vectors divided by its magnitude is the normal vector, all that...I can use it fine and I get in some applications what it equates too...


But purely in the sense of Vector A and Vector B, and their relation to the cross product I don't understand...its just random steps to me and I want to know WHY.

Thanks for trying though :\

But why is the cross product the correct way to find this? Why isn't it the first vector times 6 plus half the second vector (not that particular forumal, but any formula)

I guess I am looking for some kind of proof...Even if its in plain english just logic-ing (its a word, swear) through it.

This is the problem with classes that show how to do math but don't do the history as too why it is done that way.  Your best bet is to google or hit the library.  Maybe contact the maths department at a well known university too.  But what you want is the history as to why a particular mathematical formula works.  You'll also get a deeper understanding of the underlying fundamentals too.  Very important for understanding a subject beyond making the formulas spit out the correct answer.

I see this all the time in computer programming.  People know how to make a program but don't know the reason why they should do it this way over that way.  It is very important to get the history of the subject you are studying on top of the actually subject matter.  Would physicists learn about general relativity without learning how Einstein came up with it?

To get the determinant of a 3x3 matrix is just like doing it on a 2x2 matrix.

A B C                        A B
D E F                         C D
G H I

In a standard 2x2 matrix (the right matrix above) it is simply (A x D) - (B x C). For a 3x3 matrix (the left matrix above) it is simply (A x E x I) - (C x E x G) - cross diagonal as seen in the 2x2 matrix. Hope this makes things similar if you didn't know..

The determinant is what you can then use to work out values for XY if you are given a simultaneous equation, for example. So, I'll take (A-1) as the determinant (which is always 1 over something, eg if your AD-BC came out as 15, the determinant would be 1/15 and then whatever your matrix is, with the lead diagonal flipped (top left and bottom right in a 2x2) and the signs changed in the other two (eg. plus becomes minus) - so assuming all numbers ADBC are positive it would become D A {new line underneath} -C -B) - so the formula for a simultaneous equation when using a matrix method is:

(A-1)A X= (A-1)B

Now, to break this down:

(A-1) - the determinant as discussed above, with a fraction before it.
A - the matrix you were given
X - just for working out X/Y, not really "needed" until the last step
B - the answers of the simultaneous equation you were given (eg. 3x+2y=5 and 5x+y=2 - the B part would be at the top 5 and on the bottom 2)

I'll try to find some of my old matrix work and scan it to let you see...if you need any more help give me a shout.

____

Edit: better yet, if you can give me an example from your book I can try and work it out so you can see what I am doing..

Last edited by kylef (2008-05-20 00:48:17)

Sorry, VV, I shouldn't laugh.

But, well, I know exactly how you feel - I think I have the same approach to math as you - to get really 'comfortable' with a math concept I have to be able to visualise it and manipulate it in my head - and I have the same "but why?" questions about various aspects of vector and matrix math - particularly when it comes to vector products - I know how to calculate them and when to use them, I just can't see how they work.

Frustrating, isn't it?

I am and have already been doing tensions.

Easy too tbh, just fucking monotonous. Specially like analyzing large trusses for the forces of each member by going through each join.... uggg.
Solid works with cosmos analysis FTW...

I'm real used to the trig though, and reading off the components of forces is basicly just looking at it...Some people I work with still have to go through rules and stuff, or set everything up in a certain way so that they can apply rules and what not...what a dumb way of doing things

I think I lack understanding in this one cause linear algebra was never really the topic of any of my classes. We used it, but the closest I came to having a class on it was "Linear algebra and Differential equations"...But that was just using linear algerba in solving some differential equations.

There is like one teacher I can think of who would probably be good to talk to, but I don't go to that school anymore and its like 80 miles away...So that isn't gonna happen.

Maybe I should sign up for another math class! (Fuck that, I am done with my math requirements )

I have come to the conclusion that no one really understands. It was once written in a book somwhere and we all just go from there...

Last edited by VicktorVauhn (2008-05-20 12:36:26)

yeah, as far as torque is concerned that its the component of the force that is perpendicular to the radius X the radius...I've always seen that but I but I don't see that torque is necessarily the same concept as vector multiplication.

Good links though, I'll have to browse through that book...cool that they have it up free.