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OldExam7 - MATH 2008/09B WINTER 2008 AN OLD FINAL EXAM 1...

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MATH2008/09B WINTER2008 AN OLD FINALEXAM 1. Findthedistancebetweentheskewlines L 1 : x =2 t, y =3+4 t, z =2 t and L 2 : x = 1+ t, y =2 , z = 1+2 t . ( Hint: (a)Findtheequationoftheplane π passingthroughtheline L 2 andparalleltotheline L 1 .(b)Findthedistancefromtheline L 1 tothe plane π .) 2. Findparametricequationsofthelinethroughthepoint (1 , 2 , 3) thatisperpendic- ulartoboththe x -axisandtheline x 4 2 = y 3 1 = z 5 . 3. Aparticle has the velocity V ( t ) = (1 , 2 t,t 2 ). Letthe initialposition vector be r (0)=(0 , 0 , 0); (a)Findthepositionfunctionofthemotion; (b)Findtheunittangentvectoratthepoint parenleftbigg 1 , 1 , 1 3 parenrightbigg ; (c)Findthetangentialandnormalcomponentsoftheaccelerationvectoratthepoint parenleftbigg 1 , 1 , 1 3 parenrightbigg ; (d)Findtheunitnormalandbinormalvectorsatthepoint parenleftbigg 1 , 1 , 1 3 parenrightbigg ; (e)Findthecurvatureatthepoint parenleftbigg 1 , 1 , 1 3 parenrightbigg ; (f)Findtheradiusoftheosculatingcircleatthepoint parenleftbigg 1 , 1 , 1 3 parenrightbigg ;
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