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Unformatted text preview: Mathematics 20C Spring 2009 Final Exam Name: Section: ID: Be sure to show all work. Answers without full justification are worth no credit. Remember that you can often check your answers. You may use a single page of notes, but no other aids are allowed. This test consists of 8 questions. Each question is worth a total of 5 points. 1 /5 2 /5 3 /5 4 /5 5 /5 6 /5 7 /5 8 /5 /40 1) Let P and Q be the points P = (1 , 2 , 1) and Q = (0 , 1 , 1). Let u = ( 2 , 1 , 1 ) and v = PQ . (a) Find the cosine of the angle between u and v . (b) Find another vector w which is orthogonal to both u and v . 2) Let l ( t ) be the line containing the two points (0 , 1 , 0) and (1 , 1 , 1) and let r ( s ) be the parametric curve r ( s ) = ( s 2 , s, s 3 ) . Notice that r (1) = ( 1 , 1 , 1 ) , and so both paths go through this point. (a) Find the equation of l ( t ). (b) Find the equation of the tangent line (call it v ( s )) of r ( s ) at ( 1 , 1 , 1 ) ....
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This note was uploaded on 12/08/2011 for the course MATH 20C 20C taught by Professor Boonyeap during the Fall '07 term at UCSD.
 Fall '07
 BoonYeap

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