If l, m, n are the direction cosines of a line that is perpendicular to the lines having the direction ratios 1,2,-1 and 1,-2,1 then (l+m+n)^2=

Step-by-step solution

(l, m, n) are direction cosine of a line that is perpendicular to the lines having direction ratios (1,2,-1) and (1,-2,1) l+2 m-n=0 ...(i) l-2 m+n=0 ...(ii) Adding (i) and (ii), 2 l=0 l=0 From (i), 2 m-n=0 2 m=n Also, l^2+m^2+n^2=1 m^2+4 m^2=1 m^2= 1 5 Now, (l+m+n)^2=l^2+m^2+n^2+2(l m+m n+l n)=1+2(m n)=1+4 m^2= 9 5