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Find the shortest distance and the vecto...

Find the shortest distance and the vector equation of the line of shortest distance between the lines given by :
`(i) vec(r) = (-4 hati + 4 hatj + hatk ) + lambda ( hati + hatj - hatk)`
and `vec(r) = (-3 hati - 8 hatj - 3 hatk) + mu (2 hati + 3 hatj + 3 hatk)`
`(ii) vec(r) = (- hati + 5 hatj ) + lambda ( - hati + hatj + hatk)`
and `vec(r) = ( - hati - 3 hatj + 2 hatk) + mu ( 3 hati + 2 hatj + hatk ).`

Text Solution

Verified by Experts

The correct Answer is:
`(i) sqrt(62) ; vec(r) = ( -5 hati + 3 hatj + 2 hatk) + mu ( hati -2 hatj + 3 hatk)`
(ii) `sqrt(42) , vec(r) = (hati + 3 hatj - 2 hatk) + mu ( hati - 4 hatj + 5 hatk)`.
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