Dividing vectors in dot products

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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