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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

`sqrt30`

B

`2sqrt30`

C

`5sqrt30`

D

`-3sqrt30`

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) = (x-6)/(4)` is given by Shortest distance `=(|{:(,alpha - alpha , beta - beta, lambda - lambda),(,a_(1) , b_(1), c_(1)),(,a_(2),b_(2),c_(2)):}|)/(sqrt(sum(a_(1),b_(2)-b_(1)a_(2))^(2)))`
`=(|{:(,6,15,-3),(,3,-1,1),(,-3,2,4):}|)/(sqrt((-4-2)^(2) +(12+3)^(2)+(6-3)^(2)))`
` = (6(-6) - 15 (15) - 3(3))/(sqrt(270)) = (-270)/(sqrt(270)) = - 3 sqrt(3)`
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