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

Options

A. `sqrt30`
B. `2sqrt30`
C. `5sqrt30`
D. `3sqrt30`

Answer

d

Explanation

Given lines are `vecr = 3hati + 8hatj + 3hatk + l(3hati - hatj +hatk)`
and `vecr = - 3hati - 7hatj + 6hatk + m(-3hati + 2hatj + 4hatk)`
Required shortest distance
`=(|(6hati + 15hatj- 3hatk) .((3hati - hatj +hatk)xx(-3hati + 2hatj + 4hatk))|)/(|(3hati - hatj + hatk)xx(-3hati + 2hatj +4hatk)|)`
`=(|(6 hati + 15hatj - 3hatk).(-3hati - 15hatj + 3hatk)|)/(|-6 hati - 15hatj + 3hatk|)`
`=(36+225+9)/(sqrt(36+225+9)) = (270)/(sqrt(270)) = sqrt(270) = 3sqrt(3)`