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Unformatted text preview: MATH 23, FALL 2011 REVIEW PROBLEMS FOR EXAM 1 (COMPILED BY PROFESSOR JOHNSON) Instructions: These problems represent the types of questions you might nd on the rst 4:00 exam in this term's Math 23. They are taken directly from old exams. The best way to use this review is to choose a number of these problems to make up a (somewhat long) exam for yourself, then solve it under exam conditions, no notes, no calculator, and no looking at answers. Then, using your notes and text, grade your trial exam. Solutions will be made available soon. (1) If A = 3 i- j + 3 k , and B = 2 i + 4 j- k , nd: (a) 2 A- B , (b) The cosine of the angle between the vectors A and B . (c) The number t so that A + t B is perpendicular to i + j . (2) Find a vector perpendicular to 3 i- 2 j + k . (3) If A = 2 i + j- 3 k , and B =- 2 i + 5 j + k , nd: (a) A- 3 B , (b) A B . (c) A B . (4) Find the equation of the line of intersection of the planes x + y = 2 and y- z = 4 ....
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- Spring '06