The shortest distance between the lin...

The shortest distance between the lines `(x-3)/3=(y-8)/(-1)=(z-3)/1a n d(x+3)/(-3)=(y+7)/2=(z-6)/4` is a. `sqrt(30)` b. `2sqrt(30)` c. `5sqrt(30)` d. `3sqrt(30)`

A

`sqrt(30)`

B

`2sqrt(30)`

C

`5sqrt(30)`

D

`3sqrt(30)`

Text Solution

Verified by Experts

The correct Answer is:

D

The shortest distance between the lines
`(x-3)/3=(y-8)/(-1)=(z-3)/1`
and `(x+3)/(-3)=(y+7)/2=(z-6)/4`
is`(|(alpha^('),beta-beta^(-),gamma-gamma^(-)),(l,m,n),(l',m',n')|)/(sqrt(Sigma(mn'-nm')^(2)))`
`(|(6,15,-3),(3,-1,1),(-3,2,4)|)/(sqrt((-4-2)^(2)+(12+3)^(2)+(6-3)^(2)))` ltrbgt `=270/(sqrt(270))=sqrt(270)`
`=3sqrt(30)`

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