Given, l2+m2−n2=0 ...(i) l+m+n=0 ...(ii) By Eq. (ii), n=−(l+m) Put it Eq. (i), l2+m2=n2 ⇒l2+m2=[−(l+m)]2 ⇒l2+m2=l2+m2+2lm ⇒2lm=0 ∴ l=0 or m=0 ⇒n=−m or n=−1 ∵l2+m2+n2=1 and l2+m2+n2=1 0+m2+m2=1 and l2+l2=1 2m2=1 and l2=
1
2
m=±
1
√2
and l=±
1
√2
Direction cosine (0,
1
√2
,−
1
√2
) and (0,−
1
√2
,
1
√2
) or(
1
√2
,0,−
1
√2
) and (−
1
√2
,0,
1
√2
) ⇒ Direction of two lines ∴ (l1,m1,n1)=(0,
1
√2
,−
1
√2
) (l2,m2,n2)=(
1
√2
,0,−
1
√2
) Let θ be the angle between the lines ∴ cos‌θ=|l1l2+m1m2+n1n2|=|0+0+