Consider the plane in R^4 , calculate an orthonormal basis
[Orthogonal complement in dimension 4]. Consider the plane M in R^4 defined by the following equations:
(Image 1)
(a) Calculate an orthonormal basis (v1, v2) for M
(b) Calculate an orthonormal basis (W1, W2) for the orthogonal complement of M, N= M ?
(c) Prove that the family ? = (V1, V2,W1,W2) is an orthonormal basis for R^4

Do you need all the calculations or are you happy with the set of vectors (and the way to get them) and do the calculations yourself?

the set of vectors and how to get them is fine
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