Find the shortest distance between the lines →r=(4^i−^j)+λ(^i+2^j+^k) and →r=(^i−^j+2^k)+μ(2^i+4^j+^k)

Shortest distance between lines with vector equations →r=→a1+λ→b1 and →r=→a2+μ→b2 is ∣∣∣∣(→b1×→b2) (→a2−→a1)|→b1×→b2|∣∣∣∣
→r=4^i−^j+λ(^i+2^j+^k)
Comparing with →r=→a1+λ→b1
→→a1=4^i−^j
→b1=^i+2^j+^k
→r=^i−^j+2^k+μ(2^i+4^j+^k)
Comparing with →r=→a2+μ→b2
→→a2=^i−^j+2^k
→b2=2^i+4^j+^k
→a2−→a1=(^i−^j+2^k)−(4^i−^j)=−3^i+2^k
→b1×→b2=−2^i−^j+3^k
|→b1×→b2|=√14
→(→b1×→b2) (→a2−→a1)=(−2^i−^j+3^k) (−3^i+2^k)=−2(-3)+0+3(2)=6+6=12
Shortest distance ∣∣∣∣(→b1×→b2) (→a2−→a1)|→b1×→b2|∣∣∣∣=∣∣∣12√14∣∣∣=12/√14
Or, Shortest Distance=12/√14