# Cross Product

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• 04-22-2004
XSquared
Cross 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.
• 04-22-2004
Xterria
• 04-22-2004
XSquared
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
Xterria
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.
• 04-22-2004
XSquared
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
Xterria
details, details. I guess i'm just not good enough for you.
• 04-22-2004
golfinguy4
Or maybe you're purposely being an ass.
• 04-23-2004
Thantos
Does the truth hurt Xterria?
• 04-23-2004
InvariantLoop
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
XSquared
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
InvariantLoop
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
XSquared
What I'm looking to do is to find out exactly how the equation for cross product is created.
• 04-23-2004
InvariantLoop
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
XSquared
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
InvariantLoop
u need the proof for each 1 then
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