Let  λbe an integer. If the shortest distance between the lines x−λ=2y−1=−2z and x=y+2λ=z−λ is , then the value of λ  is __________

The given lines are x−λ2=y−1/21=z−1    x−01=y−−2λ1=z−λ1Shortest distance =722Normal vector to both lines is 2i-3j-kAλ,12,0B(0,-2λ,λ)722= projection of AB→ on common normal 722=2λ-312+2λ-λ14⇒5λ+32=72⇒5λ=-5 or 2λ=-1 or 25 ⇒λ=-1 as λ∈z⇒|λ|=1