Dividing vectors in dot products

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SUMMARY

The discussion centers on the mathematical operation of dividing vectors in the context of dot products. It clarifies that the dot product of two vectors results in a scalar, not a vector, and thus division of vectors as fractions is not valid. For example, given vectors a = (1,2) and b = (3,4), the dot product a · b equals 11, which is a scalar. Therefore, the expression a · a / b · a does not yield a vector but rather a numerical value.

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  • Familiarity with scalar and vector distinctions in linear algebra.
  • Basic knowledge of vector notation and operations.
  • Ability to perform arithmetic operations with vectors.
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  • Learn about vector normalization and its applications.
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  • Investigate other vector operations such as cross products and their geometric interpretations.
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Homework Statement


can you divide 2 vectors which are in fractions?


Homework Equations


example a . a / b . a (dot products)


The Attempt at a Solution


would it become a / b?
 
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a and b are vectors?
If so then a dot a and a dot b are not vectors, just numbers.
Example: a = (1,2) b = (3,4)
Then a dot b = 1*3 + 2*4 = 11
 

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