The angle between the lines whose direction ratios are a, b, c and b - c, c - a, a - b is

Step-by-step solution

Let the direction ratios of the two lines be represented by vectors d₁ and d₂ . d₁ = a i + b j + c k d₂ = (b - c) i + (c - a) j + (a - b) k The angle between the lines is given by = d₁ d₂ | d₁ | | d₂ | . Calculating the dot product of the direction vectors: d₁ d₂ = a(b - c) + b(c - a) + c(a - b) d₁ d₂ = ab - ac + bc - ab + ac - bc = 0 Since the dot product is zero, the vectors are perpendicular. = 0 = 90^ Answer: 90^