MATH 230 Final: Final fall 2012
15 Feb 2019
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Do not write your name on this exam! Write your netid and your student id number in the spaces provided at the top of this page. Instructions: show all of your work on the pages provided! Explain your reasoning using complete sentences and correct grammar, spelling, and punctuation. All numerical answers must be exact; e. g. , you should write instead of 3. 14, 2 instead of 1. 414, and 1. Make sure that your nal answer is clearly indicated. Check to make sure you have pages 1 - 17. Calculators, course notes, textbooks, etc. are not allowed. Suppose that u, v are two vectors in r3 such that kuk = 3, kvk = 2, and the angle between them is = . 3 . (a) (3 points) calculate u v and ku vk. (b) (5 points) calculate (u v) (u + 2v). (c) (4 points) calculate (u + 3v) (3u v).
