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.

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- 04-22-2004XSquaredCross Product
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.

- 04-22-2004Xterria
http://types.bu.edu/ool-mini-seminar/sigma.html

hope it helps. - 04-22-2004XSquared
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). - 04-22-2004Xterria
oh, lol, sorry. ok i'm pretty sure this is want you're looking for:

http://www.lfcs.inf.ed.ac.uk/reports...S-LFCS-96-345/

hope that helps. - 04-22-2004XSquared
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).

- 04-22-2004Xterria
details, details. I guess i'm just not good enough for you.

- 04-23-2004golfinguy4
Or maybe you're purposely being an ass.

- 04-23-2004Thantos
Does the truth hurt Xterria?

- 04-23-2004InvariantLoop
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**x**v**.

**u**x**v**= (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**x**v**= (u1v1 + u2v2, + .. UnVn) - 04-23-2004XSquared
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.

- 04-23-2004InvariantLoop
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.

- 04-23-2004XSquared
What I'm looking to do is to find out exactly how the equation for cross product is created.

- 04-23-2004InvariantLoop
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) . - 04-23-2004XSquared
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.

- 04-24-2004InvariantLoop
u need the proof for each 1 then