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Unformatted text preview: MAC 2313, Fall 2010 — Midterm 1 Review Problems 1 We will discuss these problems in class on Wednesday, 9/8. Solutions will be posted on the course webpage later that day. 1 Explain why the following statements are true/false in 3 dimensions. a. Two planes either intersect or are parallel. b. Two lines parallel to a plane are parallel. c. Two lines either intersect or are parallel. d. Two lines orthogonal to a third line are parallel. e. A plane and a line either intersect or are parallel. f. Two planes orthogonal to a third plane are parallel. 2 Is the angle between the vectors a = ( 3 , − 1 , 2 ) and b = ( 2 , 2 , 4 ) acute, obtuse, or right? 3 Find the area of the parallelogram whose vertices are ( − 1 , 2 , 0), (0 , 4 , 2), (2 , 1 , − 2), and (3 , 3 , 0). 4 If a and b are both nonzero vectors and a · b =  a × b  , what can you say about the relationship between a and b ? 5 Suppose proj b a = 3 i − 4 j and that the angle between a and b is obtuse. What is comp b a ?...
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 Fall '08
 Keeran
 Calculus, Dot Product

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