Question

The shortest distance between the skew lines `overliner= (6hati + 2hatj + 2hatk) + t(hati - 2hatj + 2hatk)` and `overliner = (-4hati - hatk) + s(3hati - 2hatj - 2hatk)` is ______

Options

• 9

• `40/7`

• 108

• 120

Answer 1

The shortest distance between the skew lines `overliner= (6hati + 2hatj + 2hatk) + t(hati - 2hatj + 2hatk)` and `overliner = (-4hati - hatk) + s(3hati - 2hatj - 2hatk)` is 9.

Explanation:

`overliner= (6hati + 2hatj + 2hatk) + t(hati - 2hatj + 2hatk)` and `overliner = (-4hati - hatk) + s(3hati - 2hatj - 2hatk)` 

Let `a_1 = 6hati + 2hatj + 2hatk, a_2 = -4hati - hatk,`

`b_1 = hati - 2hatj + 2hatk, b_2 = 3hati - 2hatj - 2hatk`

`overlinea_2 - overlinea_1 = -10hati - 2hatj - 3hatk`

`overlineb_1 xx overlineb_2 = 8hati + 8hatj + 4hatk`

`|overlineb_1 xx overlineb_2| = 12`

Shortest distance = `|((overlineb_1 xx overlineb_2) . (overlinea_2 - overlinea_1))/(|overlineb_1 xx overlineb_2|)|`

= `|(-108)/12|` = 9