Use the inner product u, v = 2u1v1 + u2v2 in R2 and the Gram-Schmidt orthonormalization process to transform {(2, 1), (−2, −10)} into an orthonormal basis. (Use the vectors in the order in which they are given.)

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In numerical analysis and  linear algebra, the Gram–Schmidt process is a technique for orthonormalising an array of vectors in an inner product space, while an orthonormal basis that is a finite dimension with inner product space V is a basis for V whose vectors can be classified as orthonormal, that is, they are all unit vectors as well as being orthogonal to each other.

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so, converting firstly the mixed fractions to improper fractions and then "adding".

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