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The shortest distance between the lines ...

The shortest distance between the lines `(x-2)/(3)=(y+3)/(4)=(z-1)/(5) and (x-5)/(1)=(y-1)/(2)=(z-6)/(3)`, is

A

3

B

2

C

1

D

0

Text Solution

Verified by Experts

The correct Answer is:
D
Shortest distance `|{:(,x_(2)-x_(1),y_(2)-y_(1),z_(2)-z_(1)),(,a_(1),b_(1),c_(1)),(,a_(2),b_(2),c_(2)):}|`
`" "sqrt(sum (a_(1)b_(2)-b_(1)a_(2))^(2))`
`"Now," |{:(,x_(2)-x_(1),y_(2)-y_(1),z_(2)-z_(1)),(,a_(1),b_(1),c_(1)),(,a_(2),b_(2),c_(2)):}|`
`=|{:(,5-2,1+3,6-1),(,3,4,5),(,1,2,3):}|`
`=|{:(,3,4,5),(,3,4,5),(,1,2,3):}|`
`=0" "["Two rows are identical"]`
`therefore` shortest distance=0-
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