Practicing Success
The distance between the lines r ̅ = ( ̂i + ̂j + ̂k) + λ (3 ̂i + ̂j + 2 ̂k) and r ̅ = ( ̂2i + 2 ̂j +3 ̂k) + μ (3 ̂i + ̂j +2 ̂k) is- |
d= (√20/ √14 ) d= (√22/ √14 ) d= (√23/ √14 ) d= (√28/ √14 ) |
d= (√20/ √14 ) |
The given lines are r ̅ = ( ̂i + ̂j + ̂k) + λ (3 ̂i + ̂j + 2 ̂k) and r ̅ = ( ̂2i + 2 ̂j +3 ̂k) + μ (3 ̂i + ̂j +2 ̂k) The given lines are parallel a1 ̅ =( ̂i + ̂j + ̂k), a2 ̅ = (2 ̂i + 2 ̂j +3 ̂k) and b ̅ = (3 ̂i + ̂j +2 ̂k) Therefore the distance between the two lines is given by d= mod{ b ̅ x (a2 ̅ - a1 ̅ )/ mod(b) } ⇒ d= mod{ (3 ̂i + ̂j +2 ̂k) x ( ̂i + ̂j +2 ̂k)/ √9+1+4 } ⇒ d= mod{ ( 0 ̂i + 4 ̂j +2 ̂k)/ √14 } ⇒ d= (√20/ √14 )
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