Comparing two vectors of length N - fundamental math question

To all

Not really a Mathcad specific question but a “fundamental “ math question. I know that some of the regular contributors to this forum have the expertise.

I am comparing 2 vectors {v1} and {v2} of length N using the formula

     [{v1}T*{v2}]^2 / [{v1}T{v1}*{v2}T{v2}] 

where T = Transpose

I did a check using 2 very simple vectors of length 11 so that for x = [0,1..10]

V1 = x^2 and v2 = 10*x

Using the formula I get 0.938 thus suggesting that these 2 vectors are very similar. But clearly they are not!

Has anyone got “insight” on this? It’s quite common to use this formula in some engineering field and setting-up a threshold of > 0.9 as acceptable to assume that the vectors are similar. in this case this is telling me that a stragith line is almost as good as a parabola.

Thanks

Regards

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