If ( , , ) are the Direction cosines of an angular bisector of two lines whose Direction ratios are (2,2,1) and (2,-1,-2) , then ( + + )^2=

Step-by-step solution

Given, direction ratio are (2,2,1) and (2,-1,-2) Now, angle between the lines is given by = 4-2-2 9 9 =0 = 2 So, direction cosines of two lines are ( 2 9 , 2 9 , 1 9 ) and ( 2 9 , -1 9 , -2 9 )= ( 2 3 , 2 3 , 1 3 ) and ( 2 3 , -1 3 , -2 3 ) So, required direction cosine is ( l₁-l₂ 2 2 , m₁-m₂ 2 2 , n₁-n₂ 2 2 ) aligned & = ( 0 2 1 2 , 1 2 1 2 , 1 2 1 2 ) & = (0, 1 2 , 1 2 )=( , , ) aligned Now, ( + + ) 2= ( 2 2 )^2= 4 2 =2