The shortest distance between the lines `x/2=y/2=z/1 and (x+2)/(-2) =(y-4)/(8) =(z-5)/(4)` lies in the interval

Options

A. `(2,3]`
B. `[0,1)`
C. `(3,4]`
D. `[1,2)`

Answer

A

Explanation

Given lines pass through the points having position vectors `veca_(1)=0hati+0hatj+0hatk` and `veca_(2)=-2hati+4hatj+5hatk` and are parallel to vectors `vecb_(1)=2hati+2hatj+hatk` and `vecb_(2)=-hati+8hatj+4hatk`.
`:.vecb_(1)xxvecb_(2)=|(hati,hatj,hatk),(2,2,1),(-1,8,4)|=0hati-9hatj+18hatk`
and `veca_(2)-veca_(1)=-2hati+4hatj+5hatk`
S.D.`=|((vecb_(1)xxvecb_(2)).(veca_(2)-veca_(1)))/(|vecb_(1)xxvecb_(2)|)|=|(-2xx0-36+90)/(sqrt(0+81+324))|=54/(sqrt(405))=6/(sqrt(5))`