Question

Find two unit vectors that are parallel to yz plane and are orthogonal to the vactor 3i-j+2k.

Answer 1

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 $3*0 - 1* b +2*c =0$
Condition 3: their lenght is 1, ie $\sqrt{0^2+b^2+c2} =1$
You get a system of 3 equations ( the first being easily a=0), solution of which gives you the vectors you require