The shortest distance between the lines x-1 2 = y-2 3 = z-3 4 and x-2 3 = y-4 4 = z-5 5 is

Step-by-step solution

The lines are x-1 2 = y-2 3 = z-3 4 and x-2 3 = y-4 4 = z-5 5 Comparing equations with x-x₁ a ₁ = y-y₁ ~b ₁ = z - z ₁ c ₁ and x-x₂ a ₂ = y-y₂ ~b ₂ = z - z ₂ c ₂ , we get aligned & x₁=1, y₁=2, z ₁=3 x₂=2, y₂=4, z ₂=5 & a ₁=2, ~b ₁=3, c ₁=4 a ₂=3, ~b ₂=4, c ₂=5 & | array ccc x₂-x₁ & y₂-y₁ & z₂-z₁ a ₁ & ~b ₁ & c ₁ a ₂ & ~b ₂ & c ₂ array |= | array ccc 1 & 2 & 2 2 & 3 & 4 3 & 4 & 5 array | & =1(15-16)-2(10-12)+2(8-9) & =1 & (a₁ b₂-a₂ b₁ )^2+ (b₁ c₂-b₂ c₁ )^2+ (c₁ a₂-c₂ a₁ )^2 & = (2 4-3 3)^2+(3 5-4 4)^2+(4 3-5 2)^2 & =