Division of Vector: Learn How to Perform A/B Expression

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SUMMARY

Vector division is not well-defined due to the absence of a multiplicative inverse for vectors in standard vector algebra. The discussion highlights that while scalar multiplication allows for division, vector operations such as the dot product and cross product do not support this concept. The geometric product, however, provides a framework for vector division in R^3, allowing for operations like orthogonal decomposition. The conversation emphasizes the need for a deeper understanding of vector multiplication and the limitations of traditional vector algebra.

PREREQUISITES
  • Understanding of vector algebra, including addition and scalar multiplication.
  • Familiarity with dot product and cross product operations in R^3.
  • Basic knowledge of geometric algebra and its principles.
  • Concept of multiplicative inverses in mathematical structures.
NEXT STEPS
  • Study the geometric product in geometric algebra for vector operations.
  • Explore the concept of orthogonal decomposition in vector spaces.
  • Learn about the properties and applications of the Moore-Penrose pseudoinverse.
  • Investigate advanced vector operations beyond traditional algebra, such as the wedge product.
USEFUL FOR

Students of mathematics, physicists, and engineers interested in advanced vector operations and geometric algebra applications.

  • #31
kishanachanta said:
ok.In physics we have famous formula given by Isssac Newton as F=ma where F(force) and a(accelerartion) are two vectors..if we wish to find out the value for the mass how can we divide these two vectors... means the resultant for divison of two vectors is a scalar.. i am confused...
No, you got the magnitude of the vectors, that's why you get a scalar.

Regards.
 
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  • #32
A simple way I haven't tested yet is to try to make the problem like long division.

Remember that long division implies some multiplication,

and dialectical guesswork. Good luck :)!
 

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