What is the 8D Cross Vector Product?

In summary, the conversation discusses the 8-dimensional cross vector product and the urgency of finding the answer. The person asking the question mentions the possibility of using the mathlab program to solve it. The answer is then provided, defining two vectors and the unit vector before explaining the formula for the cross product. The conversation ends with someone praising the work.
  • #1
dr-dock
8d cross vector product,URGENT

i wonder what will be the 8-dimensional cross vector product or

(N1,N2,N3,N4,N5,N6,N7,N8)x(M1,M2,M3,M4,M5,M6,M7,M8)=?

i need the answer real bad,so please answer if you can.
if you happen to have the mathlab program it might answer cause it does all the calculus with arrays or matrixes(at least that's what some say).
 
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  • #2
it's ok i have the answer!

I have the answer people!

i define two vectors a and b with dimensionality k. also i define nk as the unit vector of dimension k.

then the cross product is as such:

a x b = (a1*b1*n1 + a1*b2*n2 + ... + a1*bk*nk) +
(a2*b1*n1 + a2*b2*n2 + ... + a2*bk*nk) +
... +
(ak*b1*n1 + ak*b2*n2 + ... ak*bk*nk)

good work A?
 

FAQ: What is the 8D Cross Vector Product?

What is the definition of a "8d cross vector product?"

A "8d cross vector product" is a mathematical operation that takes two vectors in eight-dimensional space and produces a third vector that is perpendicular to both of the original vectors. It is often referred to as the vector product or cross product.

How is the "8d cross vector product" calculated?

The "8d cross vector product" is calculated using the following formula:

and are the two input vectors and are the unit vectors in the eight-dimensional space.

What is the significance of the "8d cross vector product?"

The "8d cross vector product" is important in many areas of mathematics and physics, including vector calculus, electromagnetism, and quantum mechanics. It is used to calculate the torque on a rotating object, the magnetic force on a charged particle, and the spin of a quantum particle, among other things.

Can the "8d cross vector product" be applied to vectors in other dimensions?

Yes, the "8d cross vector product" can be extended to vectors in any number of dimensions, not just eight. However, the calculation becomes increasingly complex as the number of dimensions increases.

Are there any real-world applications of the "8d cross vector product?"

Yes, the "8d cross vector product" has many practical applications in engineering, physics, and computer graphics. For example, it is used in robotics to calculate the motion of a robotic arm, in computer graphics to create 3D animations, and in navigation systems to determine the orientation of a spacecraft.

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