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Mathematics 1229A/B Midterm OCt2008

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Department
Mathematics
Course
Mathematics 1229A/B
Professor
Stefan Tohaneanu
Semester
Winter

Description
ThursdayOctober92008Mathematics1229ACODE111Page1Test11Ifu11203andv21041thenuvA30242B21003C12244D12244EnoneofABCDSolutionuv11203210411211200431122442Ifu2134andv1512thenuvA15B15C0D2E2Solutionuv2134151221153142253823Ifu312andv411thenuvA351B3111C1212D1212E157Solutionuv31241111122413314112833431114Ifu2kandv123areorthogonalperpendicularthenk11A6BCD8E822SolutionIfuandvareorthogonalthenitmustbetruethatuv0Weseethatuv2k123212k3243kThereforewemusthave243k0whichgives3k24soweneed2438k8335Ifu2kandv123arecollinearparallelthenk11A6BCD8E822SolutionIfuandvarecollinearthenitmustbetruethattheyarescalarmultiplesofoneanotheriethatucvforsomescalarvaluecWeseethatcvc12312c3c2Andsoweneed2k12c3cFromtherstcomponentwemusthave212cwhichgivesc121Usingthisvalueinthesecondcomponentweneed6131k3c36232
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