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Unformatted text preview: Math 20E Final Exam 96 points 11:30AM Friday June 11, 2004 Print Name, ID number and Section on your blue book. BOOKS and CALCULATORS are NOT allowed. Both sides of one page of NOTES is allowed. You must show your work to receive credit. 1. (12 points) Given that A B negationslash = , explain why the three vectors A | A | , A B | A B | and ( A B ) A | A B | | A | are mutually orthogonal (i.e. mutually perpendicular) unit vectors. 2. (12 points) A surface is given by R = u cos v i u sin v j + (4 u 2 ) k for 0 u 2 and | v | . (Note the minus sign on the j component.) Compute a unit normal to the surface such that the k component is positive. 3. (12 points) Find the value of the line integral integraldisplay C bracketleftbig (3 x + 4 y ) dx + (2 x + 3 y 2 ) dy bracketrightbig where C is the circle x 2 + y 2 = 4 traversed counterclockwise, that is, in the usual direction....
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