View Full Version : Cross Product

04-22-2004, 08:53 PM
Does anyone know how to derive the cross product formula from the dot product formula? My algebra teacher did it last semester, but I can't find the note, and I can't figure it out myself.

04-22-2004, 08:59 PM
hope it helps.

04-22-2004, 09:02 PM
Uhh... I'm not exactly sure what relevance that program has to my question. Let me rephrase it and see if I can clarify.

I want to know how to go from the dot product formula to the cross product formula. There is a way (I think).

04-22-2004, 09:24 PM
oh, lol, sorry. ok i'm pretty sure this is want you're looking for:
hope that helps.

04-22-2004, 09:26 PM
Eep! That's a 179-page doctorate thesis! What I want has nothing to do with calculus. It's linear algebra (vectors in 3-space).

04-22-2004, 09:29 PM
details, details. I guess i'm just not good enough for you.

04-22-2004, 11:44 PM
Or maybe you're purposely being an ass.

04-23-2004, 02:26 PM
Does the truth hurt Xterria?

04-23-2004, 03:34 PM
i took linear algebra last semester the forumla goes as follows

if u=(u1, u2, u3) and v=(v1,v2,v3) the cross product is u xv.

u xv = (u2v3 -u3v2, u3v1 - u1v3, u1v2 -u2v1) u can do turn this into matrix form if u want.

dot product aka Euclidean inner product is the same as above only with Un and Vn .
u=(u1, y2, u3..Un) and v=(v1,v2,v3,Vn) and the product is defined by
u xv = (u1v1 + u2v2, + .. UnVn)

04-23-2004, 04:05 PM
I know the formulas for dot and cross products. I'm just trying to figure out how to get the cross product formula using only the dot product formula.

04-23-2004, 05:00 PM
i think its very obvious cant u see it? they only differ in 2 things, 1 has Un and Vn which doesnt matter at all, and the other thing is that one has subtraction and the other has addition so all u gotta do is make the prog so it takes the subtraction and change it to addition and u got ur dot product.

04-23-2004, 06:32 PM
What I'm looking to do is to find out exactly how the equation for cross product is created.

04-23-2004, 09:10 PM
u already have the equation, what u need is a way to make it so the machine can understand it.

i can think of an example but no idea if this is correct.

create 2 arrays, u and v, those arrays got elements in them, u1, v1 etc.. since u already know the equation now u gotta multiply the elemts in 1 array with the elemnts of the other array in this way as the equation states (u2v3 -u3v2, u3v1 - u1v3, u1v2 -u2v1) .

04-23-2004, 09:15 PM
This has nothing to do with programming. I know the formulae, and I know how to implement them. I am just trying to figure out how you get the cross product formula from the dot product formula. Simple pen and paper.

04-23-2004, 11:25 PM
u need the proof for each 1 then

04-24-2004, 09:39 AM
yeah you need the proof for the Cross Product Formula and for the Dot Product Formula.

Hopefully they should not be too hard to find, try google. There are also many many many math websites on the net that are full of proofs.

04-24-2004, 01:51 PM
Heh, thanks. I found what I was looking for.

04-24-2004, 05:45 PM
your welcome.. :p

Zach L.
04-24-2004, 07:24 PM
I'd look at the geometrical interpretations of them first. That might provide a bit more insight than the straight out formulas for Cartesian coordinates. I'll look at it later to see if I see anything, but that might be a starting point.

04-24-2004, 07:29 PM
I believe he FOUND IT already.

04-24-2004, 08:35 PM
lurkers ........ed.

04-24-2004, 11:05 PM
This (http://hemsidor.torget.se/users/m/mauritz/math/vect/xprodpro.htm) was what I was looking for. Something that assumed no knowledge of the cross product formula that showed how to get it.