The direction cosines l, m, n of two lines are connected by the relations l + m + n = 0, lm = 0, then the angle between them is:

[a] Given d?c?s of two lines are ℓ,m,nconnected by the relation ℓ+m+n=0 and ℓm=0 Now, ℓ+m+n=0⇒ℓ=−m−n ⇒ℓ=−(m+n) And ℓm=0⇒−(m+n)m=0⇒−mn−mm=0 mn=−mn; Therefore m and m+n=0 Then ℓ1−1=m10=n11 and if ℓ+m+n=0thenℓ20=m2−1=n21 (ℓ1,m1,n1)=(−1,0,1) and (ℓ2,m2,n2)=(0,−1,1) We know that angle between them cosθ=0+0+11+0+1−−−−−−−√0+1+1−−−−−−−√=12√2√=12 cosθ=12=cos60∘⇒θ=60∘⇒θ=π3