If l, m, n are the direction cosines of the line x-1=2(y+3)=1-z , then what is l^4+m^4+n^4 equal to?

Step-by-step solution

Let x-1=(y-3)=1-z-k (Say) l=k, m= k 2 and n=k aligned & From l^2+m^2+n^2=1 & k^2+ ( k 2 )^2+k^2=1 k= 2 3 aligned aligned & l= 2 3 , m= 1 3 and n= 2 3 & l^4+m^4+n^4 & = ( 2 3 )^4+ ( 1 3 )^4+ ( 2 3 )^4= 11 27 aligned