Condition 1: given any generic vector ai+bj+cj, they're parallel to xy if a=0 Condition 2: to be orthogonal to 3i-j+2k their dot product is 0, ie [tex]3*0 - 1* b +2*c =0[/tex] Condition 3: their lenght is 1, ie [tex] \sqrt{0^2+b^2+c2} =1[/tex] You get a system of 3 equations ( the first being easily a=0), solution of which gives you the vectors you require
