# Exam1 - Name: TEST 1 answers No Calculators 1 (25 points)...

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Name: TEST 1 answers No Calculators 1: 2: 3: 4: 5: 6: 1 (25 points) Suppose that you observe a plane taking oﬀ. Initially you spot the plane at P (3 , - 5 , 3) and you are at the origin S (0 , 0 , 0). A bit later the plane is at Q (2 , - 3 , 4). How close to you will the plane go? Answer: The plane travels on a straight line parallel to v = --→ PQ = < - 1 , 2 , 1 > . See p. 883 in the book. The closest the plane will come to you is d = | -→ PS | sin θ = | -→ PS × v | | v | where -→ PS = < - 3 , 5 , - 3 > . Note -→ PS × v = ± ± ± ± ± ± ± i j k - 3 5 - 3 - 1 2 1 ± ± ± ± ± ± ± = < 11 , 6 , - 1 > hence d = p 11 2 + 6 2 + ( - 1) 2 p ( - 1) 2 + 2 2 + 1 2 = r 158 6 . 2 (15 points) Let u , v , w be three vectors with u 6 = 0. Is it true that u · v = u · w implies v = w ? If you think it is true explain why, otherwise provide a counter example. Answer: Not true. u · v = u · w is equivalent to u · ( v - w ) = 0, which means that u is perpendicular to v - w but v - w does not have to be 0. For example, let u = i , v = j and w

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## This note was uploaded on 02/03/2012 for the course MTH 234 taught by Professor Irinakadyrova during the Summer '10 term at Michigan State University.

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Exam1 - Name: TEST 1 answers No Calculators 1 (25 points)...

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