Let λ be an integer. If the shortest distance between the lines x - λ = 2 y - 1 = - 2 z and x = y + 2 λ = z - λ is 7 2 2 , then the value of λ is _______.

Step-by-step solution

x - λ 1 = y - 1 2 1 2 = z - 0 - 1 2 x - 0 1 = y + 2 λ 1 = z - λ 1 Shortest distance = a 2 → - a 1 → · b 1 → × b 2 → b 1 → × b 2 → b 1 → × b 2 → = i ^ j ^ k ^ 1 1 2 - 1 2 1 1 1 = i ^ 1 2 + 1 2 - j ^ 1 + 1 2 + k ^ 1 - 1 2 = i ^ - 3 2 j ^ + k ^ 2 = 2 i ^ - 3 j ^ + k ^ 2 b 1 → × b 2 → b 1 → × b 2 → = 2 i ^ - 3 j ^ + k ^ 14 a 2 → - a 1 → · b 1 → × b 2 → b 1 → ×