The angle between the two lines whose direction cosines satisfy the relations l + m + n = 0 and l^2 = m^2 + n^2 is

Step-by-step solution

Given the relations l + m + n = 0 and l^2 = m^2 + n^2 . From the first equation, we have l = -(m + n) . Substituting this into the second equation: (-(m + n))^2 = m^2 + n^2 m^2 + n^2 + 2mn = m^2 + n^2 2mn = 0 This gives either m = 0 or n = 0 . Case 1: If m = 0 , then l = -n . The direction ratios of the first line are proportional to (-n, 0, n) , which simplifies to (-1, 0, 1) . Case 2: If n = 0 , then l = -m . The direction ratios of the second line are proportional to (-m, m, 0) , which simplifies to (-1, 1, 0) .