रेखाओं ` vec r = hati + hatj + lamda ( 2 hati - hatj + hatk ) ` और ` vecr = 2hati+ hatj - hatk + mu ( 3 hati - 5hatj + 2 hatk ) `
के बीच की न्यूनतम दुरी ज्ञात कीजिए |

Explanation

यहाँ ` veca _ 1 = hati + hatj, " " vecb_1 = 2hati - hatj + hatk `
` vec a _2 = 2hati + hatj - hatk , vecb _ 2 = 3hati - 5hatj + 2hatk `
` veca _ 2 - veca _ 1 = ( 2 hati + hatj - hatk ) - ( hati + hatj ) = hati - hatk `
` vecb _ 1 xx vecb _ 2 = |{:( hati,, hatj,,hatk),(2,,-1,,1),(3,,-5,,2):}| `
= ` hati (-2 + 5) - hatj ( 4 - 3 ) + hatk ( - 10 + 3 ) `
` = 3 hati - hatj - 7 hatk `
और ` (vecb _ 1 xx vecb _2 )* ( veca _ 2 - veca _ 1 ) = ( 3 hati - hatj - 7 hatk )*( hati - hatk ) `
` = 3 + 7 = 10 `
अब दो रेखाओं के बीच न्यूनतम दुरी
` = |(( vecb_1 xx vecb_2 ) * (veca_2 - veca _1))/((vecb_1 xx vecb_2 )) | = |(10)/(sqrt ( 9 + 1 + 49))| = (10)/(sqrt(59)) ` मात्रक