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

Explanation

यहाँ
` veca _ 1 = hati + 2 hatj + hatk , vecb_ 1 = hati - hatj + hatk `
` veca _ 2 = 2hati - hatj - hatk , vecb _ 2 = 2hati + hatj + 2hatk `
` therefore veca _2- veca _ 1 = hati - 3 hatj - 2 hatk `
` vecb _ 1 xx vecb _ 2 = |{:(hati,,hatj,,hatk),(1,,-1,,1),(2,,1,,2):}| = - 3hati + 3hatk `
दोनों रेखाओं के बीच न्यूनतम दुरी
` = |(( veca _ 2 - veca _ 1) * ( vecb _ 1 xx vecb _ 2 ))/(| vecb _ 1 xx vecb _ 2 |) |`
` = |((hati - 3hatj - 2 hatk ) * ( - 3 hati + 3hatk ) )/(| - 3hati + 3hatk |)|`
` = |( - 3 - 6 ) /(sqrt ( 9 + 9 ) ) | = ( 9 ) /( 3 sqrt2 ) = ( 3 ) /(sqrt2 ) `