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Shortest distance between the lines `(x-1)/1=(y-1)/1=(z-1)/1a n d(x-2)/1=(y-3)/1=(z-4)/1` is equal to a. `sqrt(14)` b. `sqrt(7)` c. `sqrt(2)` d. none of these

A

`sqrt14`

B

`sqrt7`

C

`sqrt2`

D

none of these

Text Solution

Verified by Experts

The correct Answer is:
c
The given lines are parallel.

From the figure, we get
`BC=((2-1)1)/(sqrt3)+((3-1)1)/(sqrt3)+((4-4)1)/(sqrt3)`
`=(1+2+3)/(sqrt3)=2sqrt3`
`AB=sqrt(1+4+9)=sqrt14`
Shortest distance `=AB=sqrt(14-12)=sqrt(2)`
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