Algorithm for Vector Cross Product of N Dimensions

[Mike Schilling]

On Sat, 25 Aug 2007 00:35:34 GMT, "Mike Schilling"


The determinant he is speaking of is simply a mechanism that helps to
remember how to compute a cross product. This "determinant" is not a
scalar.

Check out this link

http://mathworld.wolfram.com/CrossProduct.html

and look at (3).

That's clever. Thanks.

 

[GArlington]

The cross product of two vectors is defined
only for dimension N = 3.

A formal expression for the cross product
between u = (a,b,c) and v = (p,r,q) is
u x v =
| X Y Z |
| a b c |
| p q r |
where unit vectors X = (1,0,0), Y = (0,1,0),
and Z = (0,0,1) are treated as commuting with
the scalars in this determinant formula.

Writing this out explicitly:

u x v = (br-cq,cp-ar,aq-bp)

The cross product u x v has the characteristic
of being orthogonal (perpendicular) to both u
and v. A higher dimensional analog can be
obtained from the formal expression above,
but it would require in N dimensions the input
of N-1 vectors. Hence only in three dimensions
is it the cross product of two vectors.

regards, chip

I was just wondering: what is the difference between vectors X =
(1,0,0) and Y = (1,0) and in fact Z = (1)?

 

[Wildemar Wildenburger]

I was just wondering: what is the difference between vectors X =
(1,0,0) and Y = (1,0) and in fact Z = (1)?

Uhm ... the dimension?

/W