MATH115F19Quiz03Solutions.pdf - MATH 115 Fall 2019 Quiz 3...

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MATH 115 Fall 2019: Quiz 3 Solutions1. Let~u,~vRnand~z, ~wCnwhere~u=123,~v=2-11,~z=1 +j1-j3and~w=2 +j1-j(a) Compute the area of the parallelogram determined by~uand~v.(b) Compute proj~v~uand perp~v~u.(c) Computeh~z, ~wiandh~w, ~zi.(d) Computek~zk.Solution.
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2.(a) Consider a line with direction vector~d. Find the vector equation of this line given that it lies inthe planex1+x2+x3= 4, contains the pointP(-2,1,5), and~dis orthogonal to~v=32-2.(b) Consider the plane that contains the two lines121+t21-3, tR-112+s-4-26, sR

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