l + m + n = 0, ⇒ l = - m - n and l2+m2−n2=0 ∴ (−m−n)2+m2−n2=0⇒2m2+2mn=0 ⇒ 2m(m + n) = 0 ⇒ m = 0 or m + n = 0 If m = 0, then l= -n ∴
l1
−1
=
m1
0
=
n
1
and if m + n = 0 ⇒ m = -n, then l=0 ∴
l2
0
=
m2
−1
=
n2
1
i.e., (l1,m1,n1)=(−1,0,1) and (l2,m2,n2)=(0,−1,1) ∴ cos‌θ=