MATH 2210 Midterm: MATH 2210 Cornell 2210 2013 Fall prelim2 Exam
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Math 2220 prelim 1: solutions (1) state whether the following are true or false and justify your answer: (a) the vectors (5, 7, 1) and (1, 0, 5) are orthogonal. True, since (5, 7, 1) (1, 0, 5) = 0. (b) the angle between the vectors (0, 0, 1) and (5, 7, 1) is . If denotes the angle, then the dot product is. 1 = k(0, 0, 1)kk(5, 7, 1)k cos( ) which implies cos( ) 6= cos( ) = 1. (c) if l1 and l2 are lines in r3 then there exists a plane containing l1 and l2. For example, there is no plane containing both the line x = y = 0 and the line x = 1, z = 0. (d) if a and b are vectors in r3 then ka bk kakkbk. True. ka bk = kakkbk sin( ) where is the smaller angle between a and b.
