The shortest distance between the skew lines r =( i +2 j +3 k )+t( i +3 j +2 k ) and r =(4 i +5 j +6 k )+t(2 i +3 j + k ) is

Step-by-step solution

Given skew lines are r =( i +2 j +3 k )+t( i +3 j +2 k ) and r =(4 i +5 j +6 k )+t(2 i +3 j + k ) Here, aligned & a ₁= i +2 j +3 j & b ₁= i +3 j +2 k & a ₂=4 i +5 j +6 k & b ₂=2 i +3 j + k aligned and b ₂=2 i +3 j + k Now, 0 aligned a ₂- a ₁ & =4 i +5 j +6 k -( i +2 j +3 k ) & =3 i +3 j +3 k aligned and aligned b ₁ b ₂ & = | array ccc i & j & k 1 & 3 & 2 2 & 3 & 1 array | & = i (3-6)- j (1-4)+ k (3-6) & =-3 i +3 j -3 k aligned The shortest distance between skew lines aligned & = | ( a ₂- a ₁ ) ( b ₁ b ₂ ) | | b ₁ b