consider a1 = (1, 1, 2)T and a2 = (-2, 0, 1)T

i am looking for a b3 such that b1 = 1/length(a1) * a1 and b2 = 1/length(a2) * a2

and need a b3 that is orthogonal to these.Why does it not matter if I use (-1, 1 , 4)T (i.e. a1 + a2 with one component changed) or just using e1 (1, 0, 0)T?