If (l₁, m₁, n₁ ) and (l₂, m₂, n₂ ) are direction cosines of ( O A ) and (O B ) such that ( A O B= ), where (O ) is the origin, then the direction cosines of the internal angular bisector of ( A O B ) are

Step-by-step solution

( l₁ l₂+m₁ m₂+n₁ n₂= ) Through origin (O ) draw two lines parallel to given lines and take two points on each at a distance (r ) from (O ) and a point (R ) on (Q O ) produced so that (O R=r ) Then, the coordinates of (P, Q ) and (R ) are ( (l₁ r, m₁ r, n₁ r ), (l₂ r, m₂ r, n₂ r ) ) and ( (-l₂ r,-m₂ r,-n₂ r ) ) respectively. If (A, B ) be the mid-points of (P Q ) and (P R ), then (O A ) and (O B ) are along the bisectors of the lines direction ratios of (O A ) are (l₁+l₂, m₁+m_ 2, , n₁+n₂ ) (D R ) 's of (O B ) are (