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dot product

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hello.
I must analize a lot of dot product.
These dot product are from the x axes {1,0} and a 2d point in the space.
Is possible that each dot product for each two point in my space is unique?
there is a method for make unique the dot product result of each dot from {1,0} to each point in the space?
or there are some incongruency(two different dot product have a scalar that is the same of and two different vectors?
and with the normalization?
i can avoid this problem?
thanks.

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I'm not exactly sure what you are trying to say, so correct me if I misinterpret you. You are saying that you are analysing dot products between the x unit vector (1,0) and a collection of vectors representing points in 2D space. In this case the dot product is simply the x co-ordinate of the vector, so if you had vectors (3,0), (3,10) and (3,-10) then they would all have the same dot product. If you normalise the collection of vectors you still have problems if some of the vectors are parallel with each other (for example, the vectors (3,4) and (6,8) would both normalise to (0.6,0.8)). Hopefully this helps.

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Dot products aren't invertible since they aren't bijective.

If a, b are vectors then the solution a.b = k defines a hyperplane (i.e. a line in 2d a plane in 3d) so there are infinitely many points satisfying the equation.

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