Cross product imaginary numbers

Click For Summary
SUMMARY

The discussion centers on the properties of the cross product in vector mathematics, specifically regarding the manipulation of imaginary numbers. The user questions the validity of expressing the cross product of imaginary units and constants, leading to the conclusion that while the cross product is linear, it is not associative. The correct interpretation involves using parentheses to clarify the order of operations, as demonstrated by the expressions (k x k) x E equating to zero, while k x (k x E) yields a non-zero result if k and E are not parallel.

PREREQUISITES
  • Understanding of vector mathematics and operations
  • Familiarity with the properties of cross products
  • Knowledge of imaginary numbers and their manipulation
  • Basic principles of linear algebra
NEXT STEPS
  • Study the properties of vector cross products in depth
  • Learn about the implications of linearity in vector operations
  • Explore the concept of associativity in mathematical operations
  • Investigate the geometric interpretation of cross products in three-dimensional space
USEFUL FOR

Mathematicians, physics students, and anyone interested in advanced vector calculus and the manipulation of imaginary numbers in mathematical contexts.

thegirl
Messages
40
Reaction score
1
Hi,

I was just wondering if you have a cross product can you multiply out the constants and put them to one side.

So ik x ik x E is equal to i^2(k x k x E) therefore is equal to -k x k x E.

Is that correct?
 
Mathematics news on Phys.org
Yes, the cross product is linear. However, writing something like A x B x C is not well defined as the cross product is not associative. You have to write either A x ( B x C) or (A x B) x C. Generally (k x k) x E = 0 while k x (k x E) will be non-zero if k and E are not parallel.
 
Ahhhh yes the brackets! Thank You!
 

Similar threads

High School Imaginary Pythagoras
  • · Replies 13 ·
Replies
13
Views
1K
Undergrad Alternating Harmonic Numbers are cool, spread the word!
  • · Replies 4 ·
Replies
4
Views
3K
Undergrad Why does the cross product operation adhere to the right-hand rule?
  • · Replies 8 ·
Replies
8
Views
2K
Undergrad What is the role of geometry and dimensional operations?
  • · Replies 3 ·
Replies
3
Views
2K
High School Deriving law of sines from cross product
  • · Replies 4 ·
Replies
4
Views
5K
Undergrad Extend Euler Product Convergence Over Primes: Basic Qs
  • · Replies 0 ·
Replies
0
Views
2K
Undergrad Explaining imaginary numbers to laypeople
  • · Replies 29 ·
Replies
29
Views
4K
Undergrad Is e^pi a unique transcendental, or perhaps not transcendental?
  • · Replies 1 ·
Replies
1
Views
2K
Obtain an equation of the plane in the form ##px+qy+rz=d##
  • · Replies 5 ·
Replies
5
Views
1K
Undergrad Video on imaginary numbers and some queries
  • · Replies 3 ·
Replies
3
Views
2K