The shortest distance between lines r =( i +2 j - k )+ (2 i + j -3 k ) and r =(2 i - j +2 k )+ ( i - j + k ) is

Step-by-step solution

aligned & r =( i +2 j - k )+ (2 i + j -3 k ) and & r =(2 i - j +2 k )+ ( i - j + k ) & Let a ₁= i +2 j - k , a ₂=2 i - j +2 k & b ₁=2 i + j -3 k , b ₂= i - j + k & a ₂ - a ₁ = i -3 j +3 k & b ₁ b ₂=-2 i -5 j -3 k & | b ₁ b ₂ |= 38 aligned aligned Shortest distance & = | ( b ₁ b ₂ ) ( a ₂- a ₁ ) | b ₁ b ₂ | | & = | 4 38 |= | 2 2 19 | units aligned