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- What postulates of Euclid enables the geometric dot product

Hello

As you know, the geometric definition of the dot product of two vectors is the product of their norms, and the cosine of the angle between them.

(The algebraic one makes it the sum of the product of the components in Cartesian coordinates.)

I have often read that this holds for Euclidean Space.

I know that there are 5 postulates of Euclidean Space.

However, I am unable to connect the geometric definition of the dot product as deriving from those five postulates.

Can someone explain why those five postulates lend themselves to an understanding of the geometric definition of the dot product

As you know, the geometric definition of the dot product of two vectors is the product of their norms, and the cosine of the angle between them.

(The algebraic one makes it the sum of the product of the components in Cartesian coordinates.)

I have often read that this holds for Euclidean Space.

I know that there are 5 postulates of Euclidean Space.

However, I am unable to connect the geometric definition of the dot product as deriving from those five postulates.

Can someone explain why those five postulates lend themselves to an understanding of the geometric definition of the dot product