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प्रश्न
Find the shortest distance between the lines
`(x+1)/7 = (y + 1)/(-6) = (z + 1)/1 and (x - 3)/1 = (y - 5)/(-2) = (z - 7)/1`
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उत्तर
Shortest distance between the lines
= 4(−6 + 2) − 6(7 − 1) + 8(−14 + 6)
= − 16 − 36 − 64
= − 116
and `(b_1c_2 - b_2c_1)^2 + (c_1a_2 - c_2a_1)^2 + (a_1b_2 - a_2b_1)^2`
= (−6 + 2)2 + (1 − 7)2 + (−14 + 6)2
= 16 + 36 + 64
= 116
∴ shortest distance between the given lines
`|(-116)/sqrt(116)|`
`sqrt(116)`
= `2sqrt(29)` units
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