Why is the Gram-Schmidt process used?

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Why is this process used to construct an orthonormal basis? Why can’t an orthonormal basis be found from a basis by just taking the norm of each of each and dividing the respective basis vector by it?The notes I have on this just state it is used, and shows the method

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If you were to just divide each vector in a basis by their norm, they would be unit norm, but not orthogonal.