If the lines x - 1 2 = 2 - y - 3 = z - 3 α and x - 4 5 = y - 1 2 = z β intersect, then the magnitude of the minimum value of 8 α β is _____.

Step-by-step solution

Let, L 1 = x - 1 2 = y - 2 3 = z - 3 α = λ L 2 = x - 4 5 = y - 1 2 = z - 0 β = μ For point of intersection 2 λ + 1 = 5 μ + 4         . . .   i 3 λ + 2 = 2 μ + 1           . . .   ii α λ + 3 = β μ + 0           . . .   iii From i and ii , we get   λ = μ = - 1 Now, from iii , we get   α - β = 3 Let y = 8 α β ⇒ y = 8 α α