Let R4 have the Euclidean inner product
(a) Find a vector in R4 that is orthogonal to u1 = (1,0,0,0) and u4 = (0,0,0,1) and makes equal angles with u2 = (0,1,0,0) and u3 = (0,0,1,0).
(b) Find a vector x = (x1,x2, x3, x4) of length 1 that is orthogonal to u1 and u4 above and such that the cosine of the angle between x and u2 is twice the cosine of the angle between x and u3.