The shortest distance between the lines `(x-x_(1))/(a_(1)) =(y-y_(1))/(b_(1))=(z-z_(1))/(c_(1)) and (x-x_(2))/(a_(2))=(y-y_(2))/(b_(2))=(z-z_(2))/(c_(2))` is `|{:(,x_(1)-x_(1),y_(2)-y_(1),z_(2)-z_(1)),(,a_(1),b_(1),c_(1)),(,a_(2),b_(2),c_(2)):}|`/A Here, A refers to

Options

A. `(b_1c_(2)-b_(2)c_(1))^2-(c_(1)a_(2)-c_(2)a_(1))^(2)+(a_(1)b_(2)-a_(2)b_(1))^(2)`
B. `(b_1c_(2)-b_(2)c_(1))^2+(c_(1)a_(2)-c_(2)a_(1))^(2)+(a_(1)b_(2)-a_(2)b_(1))^(2)`
C. `sqrt((a_(1)b_(2)-a_(2)b_(1))^(2)+(b_(1)c_(2)-b_(2)c_(1))^2+(c_(1)a_(2)-c_(2)a_(1))^(2))`
D. None of these

Answer

C

Explanation

The shortest distance between the line
`(x-x_(1))/(a_(1)) =(y -y_(1))/(b_(1)) =(z -z_(1))/(c_(1))` and `(x-x_(2))/(a_(2)) = (y-y_(2))/(b_(2)) = (z -z_(1))/(c_(1))` in cartesian froms is