If the direction cosines of two lines are 2 3 , 2 3 , 1 3 and 5 13 , 12 13 , 0 , then identify the direction ratios of a line which is bisecting one of the angle between them.

Step-by-step solution

Given, the direction cosines of two lines are 2 3 ,   2 3 ,   1 3 and 5 13 ,   12 13 ,   0 . We know that, the direction ratios of the line bisecting the angle between the lines whose direction cosines are l 1 ,   m 1 ,   n 1 and l 2 ,   m 2 ,   n 2 are proportional to ⟨ l 1 + l 2 ,   m 1 + m 2 ,   n 1 + n 2 ⟩ . Hence, the required direction ratios are proportional to ⟨ 2 3 + 5 13 ,   2 3 + 12 13 ,   1 3 + 0 ⟩ = ⟨ 41 39 ,