InterviewSolution
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InterviewSolution
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The shortest distance between the lines ` r = ( - hati - hatj - hatk ) + lamda ( 7 hati - 6 hatj + hatk ) and r = ( 3 hati + 5 hatj + 7 hatk ) + mu ( hati - 2 hatj + hatk ) `A. ` sqrt ( 29 ) ` unitsB. 29 unitsC. ` ( 2 9 ) / ( 2 ) ` unitsD. ` 2 sqrt ( 29 ) ` units |
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Answer» Correct Answer - D The given lines are ` r = - hati - hatj - hatk+ lamda ( 7 hati - 6hatj + hatk ) ` and ` r = ( 3 hati + 5 hatj + 7 hatk ) + mu ( hati - 2hatj + hatk ) ` where, ` a _ 1 = - hati - hatj - hatk , b _ 1 = 7 hati - 6 hatj + hatk ` and ` a_ 2 = 3hati + 5 hatj + 7 hatk , b _ 2 = hati - 2 hatj + hatk ` Now, ` a _ 2- a _ 1 = ( 3 hati + 5hatj + 7 hatk ) - ( - hati - hatj - hatk ) ` ` = 4 hati + 6hatj + 8 hatk ` and ` b _ 1 xx b _ 2 = |{:( hati , hatj , hatk ) , ( 7, - 6, 1 ) , ( 1, -2, 1 ) :}| ` ` = hati ( - 6 + 2 ) - hatj ( 7 - 1 ) + hatk ( -14 + 6 ) ` ` = - 4hati - 6 hatj - 8 hatk ` ` rArr | b _ 1 xx b _ 2 | = sqrt(( - 4 ) ^ 2 + ( - 6 ) ^ 2 + ( -8 ) ^ 2 ) ` ` = sqrt ( 16 + 36 + 64 ) = sqrt ( 116 ) ` ` therefore ` Shortest distance between the given lines ` d= | (( b _ 1 xx b _ 2 ) * ( a _ 2 - a _ 1 ) ) / ( |b _ 1 xx b _ 2 | ) | ` ` (| ( - 4hati - 6 hatj - 8 hatk ) * ( 4hati + 6 hatj + 8 hatk )| ) / ( sqrt ( 116 ) ) ` ` = (| ( -4 ) xx 4 + ( - 6 ) xx 6 + ( - 8 ) xx 8 | ) /( sqrt ( 116 )) ` ` = (116 ) / ( sqrt (116 )) = sqrt (116) = 2 sqrt (29 ) ` units |
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