L(i/1)+M(j/1) +N(i+j)/root 2.

Now the angular bisector of a and b is given by a/mod(a) +b/mod(b)

implies i+j

now projection of the 1st vector on i+j  is {L(i/1)+M(j/1) +N(i+j)/root 2}cos(angle between the vectors).

See if the method works.