If 2,3,4 and 1,2,3 are direction ratios of OA→andOB→, then the direction cosines of a line perpendicular to both the lines OA→ andOB→ are

The direction ratio of any line perpendicular to both lines OA,OB is along the vectorOA¯×OB¯It implies,OA¯×OB¯=ijk234123=i9−8−j6−4+k4−3=i−2j+kHence, the direction ratios of the line perpendicular to the lines are1,−2,1 Therefore, the required direction cosines are  16,−26,16