The correct option is D l1+l2,m1+m2,n1+n2
Let direction cosines of OA=(l1,m1,n1) and direction cosines of OB=(l2,m2,n2).
Taking two points on l and m such that OA=OB=r
Let C be the mid-point of AB. Then, OC is the bisector of the angle AOB.
Now, coordinates of A are (l1r,m1r,n1r) and coordinates of B are (l2r,m2r,n2r).
∴ the coordinates of C are
Hence, the direction cosines of OC are proportional to l1+l2,m1+m2 and n1+n2.