XSquared

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.

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XSquared

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.

Xterria

04-22-2004, 08:59 PM

http://types.bu.edu/ool-mini-seminar/sigma.html

hope it helps.

hope it helps.

XSquared

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).

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

Xterria

04-22-2004, 09:24 PM

oh, lol, sorry. ok i'm pretty sure this is want you're looking for:

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

hope that helps.

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

hope that helps.

XSquared

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).

Xterria

04-22-2004, 09:29 PM

details, details. I guess i'm just not good enough for you.

golfinguy4

04-22-2004, 11:44 PM

Or maybe you're purposely being an ass.

Thantos

04-23-2004, 02:26 PM

Does the truth hurt Xterria?

InvariantLoop

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)

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)

XSquared

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.

InvariantLoop

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.

XSquared

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.

InvariantLoop

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) .

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) .

XSquared

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.

InvariantLoop

04-23-2004, 11:25 PM

u need the proof for each 1 then

DavidP

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.

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.

XSquared

04-24-2004, 01:51 PM

Heh, thanks. I found what I was looking for.

Xterria

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.

Lurker

04-24-2004, 07:29 PM

I believe he FOUND IT already.

Xterria

04-24-2004, 08:35 PM

lurkers ........ed.

XSquared

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.

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