Verify the Product Rule for cross products

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SUMMARY

The discussion centers on verifying the Product Rule for cross products in vector mathematics. The initial equation presented, which equates the cross product of two vectors to a scalar involving cosine, is incorrect. Participants emphasize that the result of a cross product is a vector, not a scalar, and caution against using cosine in this context. Additionally, they highlight the importance of using distinct symbols for cross products to avoid confusion.

PREREQUISITES
  • Understanding of vector operations, specifically cross products
  • Familiarity with vector notation and terminology
  • Knowledge of trigonometric functions and their application in vector mathematics
  • Basic principles of vector magnitudes
NEXT STEPS
  • Study the properties of cross products in vector algebra
  • Learn about the geometric interpretation of cross products
  • Explore the implications of parallel vectors on cross product results
  • Review vector notation conventions to avoid common pitfalls
USEFUL FOR

Students and educators in physics or mathematics, particularly those focusing on vector calculus and linear algebra concepts.

andyk23
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cross products= vector(a)*vector(b)=Magnitude(a)*magnitude(b)*cos(theta)
I'm having trouble on how to get started...
 
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first that equation is not correct

you probably want to help yourself by using a different symbol for the cross product like x

and you want to be careful with your magnitudes, as the result of a cross product is a vector, which can't be equal to a scalar
 
also are you sure that's a cos? what's the cross product of 2 parallel vectors?
 

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