The shortest distance between lines r =(2 i - j )+ (2 i + j -3 k ) and r =( r - j +2 k )+ (2 i + j -5 k ) is

Step-by-step solution

We have lines r =(2 i - j )+ (2 i + j -3 k ) and r =( r - j +2 k )+ (2 i + j -5 k ) Let a =2 i - j and b = i - j +2 k AB =- i +2 k Vector perpendicular to given lines is n = | array ccc i & j & k 2 & 1 & -3 2 & 1 & -5 array |= i (-5+3)- j (-10+6)+ k (2-2)=-2 i +4 j Shortest distance between given lines = AB n | n | = (- i +2 k ) (-2 i +4 j ) (-2)^2+(4)^2 = 2 20 = 1 5