The shortest distance is given by,
= |

(A2−A1).(B1×B2)

|B1×B2|

|
A2−A1 = (

^

i

−

^

j

−2

^

k

) - (4

^

i

−

^

j

) = - 3

^

i

−2

^

k

B1×B2 = |

^ i	^ j	^ k
1	2	−3
2	4	−5

| = 2

^

i

−

^

j

(A2−A1) . (B1×B2) = (−3

^

i

−2

^

k

) . (2

^

i

−

^

j

) = - 6
|B1×B2| = √22+12 = √5
so shortest distance between two lines = |

−6

√5

| =

6

√5

units