The coordinates of P,Q and R are (l1r,m1r,n1r),(l2r,m2r,n2r) and (l3r,m3r,n3r) respectively. The A and B are midpoints of PQ and PR, then OA and OB are bisectors line of direction ratios of OA are l1+l2,m2+m2,n1+n2 and for OB are l1−l2,m2−m2,n1−n2 Now, ∑(l1+l2)2=1+1+2cosθ =2(1+cosθ) =4cos2