Consider R4 with the Euclidean inner product.
(a) Find a unit vector that is orthogonal to the vectors u = (2, 1, −4, , 0), v = (−1, −1, 2, 2), and w = (3, 2, 4, 5).
(b) Let W be the subspace of R4 spanned by the vectors u, v, and w. Find a basis for the orthogonal complement of W.
For part a, how do I find the orthogonal unit vector for u,v and w? I've only ever found orthogonal unit vectors for 2 vectors, not 3.
For part b, how do you find the orthogonal complement of a basis?
Any help would be appreciated.