# 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