23sp12-final-solutions - MATH 23 SPRING 2012 FINAL EXAM...

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MATH 23, SPRING, 2012, FINAL EXAM SOLUTIONS(1) For vectorsA= 2i+ 3j-kandB=-i+ 3k, find:(5 points per part)(a)A-2B.
(b)A·B.
(c) The vector projectionprojBAofAontoB.
(d)A×B.
(2) Find the line of intersection between the planesP1defined by2x+ 3y-z= 0andP2defined byx+ 3y+z= 1.(10 points)1
MATH 23, SPRING, 2012, FINAL EXAM SOLUTIONS2
(3) Find the arclength of the curver(t) =etcos(t)i+etsin(t)j,t[0,2π].(10 points)

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