Hi DEvens
vector <1/√3,1/√3,1√3> and <1/√2,0,-1/√2> have a dot product equal to zero, and the vector <-881/2158,881/1079,-881/2158> was the result of crossing a and b sso te should be all orthogonal to one another but I could be wrong. Your three formulas are very interesting but I am confused...