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# notes001 (31) - MATH 2203&Exam 1(Version 2 Solutions S...

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Unformatted text preview: MATH 2203 &Exam 1 (Version 2) Solutions September 15, 2010 S. F. Ellermeyer Name Instructions. Your work on this exam will be graded according to two criteria: mathe- matical correctness and clarity of presentation . In other words, you must know what you are doing (mathematically) and you must also express yourself clearly. In particular, write answers to questions using correct notation and using complete sentences where appropriate. Also, you must supply su¢ cient detail in your solutions (relevant calculations, written explanations of why you are doing these calculations, etc.). It is not su¢ cient to just write down an &answer¡with no explanation of how you arrived at that answer. As a rule of thumb, the harder that I have to work to interpret what you are trying to say, the less credit you will get. You may use your calculator but you may not use any books or notes. 1. Show how to £nd the distance between the points P (4 ; & 2 ; 3) and P 1 (2 ; & 2 ; 4) . Solution: The distance between these points is & & & &&! P P 1 & & & = q (2 & 4) 2 + ( & 2 & ( & 2)) 2 + (4 & 3) 2 = q ( & 2) 2 + 0 2 + 1 2 = p 5 . (a) Find the unit vector obtained by rotating the vector h ; 1 i through an angle of 120 & counterclockwise about the origin. (b) Express the vector v = 5 i + 1 5 j as the product of its magnitude and direction....
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notes001 (31) - MATH 2203&Exam 1(Version 2 Solutions S...

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