InterviewSolution
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InterviewSolution
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Consider the lines ` L _ 1 : ( x - 1 )/ ( 3 ) = ( y + 2 ) / ( 1 ) = ( z + 1 ) / ( 2 ) ` ` L _ 2 : ( x - 2) / ( 1 ) = ( y + 2 ) / ( 2 ) = ( z - 3 )/ ( 3 ) ` The unit vector perpendicular to both ` L _ 1 and L_ 2 ` isA. ` ( 1 ) / ( sqrt (99)) ( - hati + 7 hatj +7hatk ) `B. ` ( 1 ) / ( 5 sqrt3) ( - hati - 7 hatj + 5 hatk ) `C. ` ( 1 ) / ( 5sqrt 3 ) ( - hati+ 7 hatj + 5 hatk ) `D. ` ( 1 ) /( sqrt ( 99)) ( 7 hati - 7hatj - hatk ) ` |
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Answer» Correct Answer - B Lines `L _ 1 and L _ 2 ` are parallel to the vectors ` b _ 1 = 3 hati + hatj + 2 hatk and b _ 2 = hati + 3 hatj + 3 hatk ` respectively. Therefore, a unit vector perpendicular to both `L _ 1 and L _ 2 ` is ` hatn = ( b _ 1 xx b _ 2 ) / ( | b _ 1 xx b _ 2 | ) ` ` b _ 1 xx b _ 2 = |{:( hati , hatj , hatk ) , ( 3, 1, 2 ) , (1, 2, 3 ) :}| = - hati - 7 hatj + 5hatk ` ` therefore hatn = ( 1 ) / ( 5sqrt 3 ) ( - hati - 7 hatj + 5 hatk ) ` |
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