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Question
Find the shortest distance between the following lines:
`vecr = (hati + hatj - hatk) + s(2hati + hatj + hatk)`
`vecr = (hati + hatj - 2hatk) + t(4hati + 2hatj + 2hatk)`
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Solution
Here, the lines are parallel.
The shortest distance = `(|(veca_2 - veca_1) xx vecb|)/|vecb|`
= `(|(3hatk) xx (2hati + hatj + hatk)|)/sqrt(4 + 1 + 1)`
`(3hatk) xx (2hati + hatj + hatk) = |(hati, hatj, hatk),(0, 0, 3),(2, 1, 1)| = -3hati + 6hatj`
Hence, the required shortest distance = `(3sqrt(5))/sqrt(6)` units.
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