Given relations are:

⇒ l²+m²–n²=0 ……(1)

⇒ l+m+n=0

⇒ l=–m–n……(2)

Substituting (2) in (1) we get,

⇒ (–m–n)²+m²–n²=0

⇒ m²+n²+2mn+m²–n²=0

⇒ 2m²+2mn=0

⇒ 2m(m+n)=0

⇒ 2m=0 or m+n=0

⇒ m=0 or m=–n ……(3)

Substituting value of m from(3) in (2)

For the 1^st line:

⇒ l=–0–n

⇒ l=–n

The Direction Ratios for the first line is (–n,0,n)

For the 2^nd line:

⇒ l=–(–n)–n

⇒ l=n–n

⇒ l=0

The Direction Ratios for the second line is (0,–n,n)

We know that the angle between the lines with direction ratios proportional to (a₁,b₁,c₁) and (a₂,b₂,c₂) is given by:

⇒

Using the above formula we calculate the angle between the lines.

Let be the angle between the two lines given in the problem.

⇒

⇒

⇒

⇒

⇒

∴ The angle between given two lines is .