The direction cosines of the line x−1l=y+1l+1=z−1l

If ⟨l,m,n⟩ are direction cosines of a line then l2+m2+n2=1Hence,  l2+(l+1)2+l2=1It implies that  3l2+2l=0⇒l(3l+2)=0⇒l=0,−23Therefore, the direction cosines are ⟨−23,13,−23⟩