The shortest distance between the line 1+x=2y=-12z and x=y+2=6z-6 is

Options

A. 1
B. 2
C. 3
D. 4

Answer

B

Explanation

Given lines are `(x +1)/(12) = (Y)/(6) = (z)/(-1)`
and `(x)/(6) =(y+2)/(6) = (z-1)/(1)`
The shortest distance between two line is
`d=(|{:(,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((a_(1)b_(2)-b_(1)a_(2))^(2) +(b_(1)c_(2)-b_(2)c_(1))^(2) +(c_(1)a_(2)-a_(1)c_(2))^(2)))`
`d(|{:(,1,-2,1),(,12,6,-1),(,6,6,1):}|)/(sqrt((72 - 36)^(2) +(6+6)^(2) +(-6-12)^(2)))`
` = (1(6+6)+2(12+6)+1(72-36))/(sqrt(1296+144+324)) = (84)/(42) = 2`