Given that the lines L₁: r = + - k + (3 - ) and L₂: r =4 - k + (2 +3 k ) are neither skew nor parallel. Then the shortest distance between the lines is

Step-by-step solution

The lines are given by L₁: r = a ₁ + b ₁ and L₂: r = a ₂ + b ₂ , where a ₁ = i + j - k , b ₁ = 3 i - j , a ₂ = 4 i - k , and b ₂ = 2 i + 3 k . The problem states that the lines are neither skew nor parallel. Since they are not parallel, they must be intersecting. For intersecting lines, the shortest distance between them is 0 . To verify, we check if the lines intersect by setting a ₁ + b ₁ = a ₂ + b ₂ : i + j - k + (3 i - j ) = 4 i - k + (2 i + 3 k ) Equating components: 1) 1 + 3 = 4 + 2 3 - 2 = 3 2) 1 - = 0 = 1 3