The distance between the parallel lines r¯=2i¯+3j¯−k¯+λ(i¯−j¯+2k¯) and r¯=−3i¯+4j¯+k¯+μ(i¯−j¯+2k¯) is

a¯1=2i¯+3j¯−k¯, a¯2=−3i¯+4j¯+k¯, b¯=i¯−j¯+2k¯, a¯1−a¯2=5i¯−j¯−2k¯b¯×(a¯1−a¯2)=i¯j¯k¯1−125−1−2=4i¯+12j¯+4k¯|b¯×(a¯1−a¯2)|=176, |b¯|=6Distance = |b¯×(a¯1−a¯2)||b¯|=1766=2223