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hwsol_3

# hwsol_3 - w"\$ 0 w n v" sin cos cos sin" 0 so n...

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Homework Assignment 3 - (10.3) - Solutions Page (1) Page 811: 5, 13, 17, 19, 20*, 23, 25, 26*, 29, 33, 35, 39, 40*, 42*, 45* 20. a ! " i ! # 3 j ! ! 2 k ! , b ! " 2 i ! ! 3 k ! a ! ! b ! " i ! # 3 j ! ! 2 k ! ! 2 i ! ! 3 k ! " 2 # 0 # 6 " 8 " 0 || a ! || " 1 # 3 2 # " ! 2 # 2 " 14 , b ! " 2 2 # " ! 3 # 2 " 13 cos ! " a ! ! b ! || a ! || b ! " 8 14 13 " 0.593, ! " cos ! 1 " 0.593 # " 0.93 26. a ! " 3 i ! , b ! " 6 j ! ! 2 k ! a ! ! b ! " 3 i ! 6 j ! ! 2 k ! " 0 So, a ! and b ! are orthogonal. 40. a ! "\$ 3,2,0 % , b ! "\$ ! 2,2,1 % a ! ! b ! " ! 6 # 4 " ! 2, b ! " " ! 2 # 2 # 2 2 # 1 " 3 comp b ! a ! " a ! ! b ! b ! " ! 2 3 proj b ! a ! " comp b ! a ! 1 b ! b ! " a ! ! b ! b ! 2 b ! " ! 2 9 \$ ! 2,2,1 %"\$ 4 9 , ! 4 9 , ! 2 9 % 42. W " Fd " " 40 # cos " 6 " 5280 # " 105600 3 " 182904.6 foot-pounds 45. F ! "\$ 30,20 % , d ! "\$ 24,10 % W " comp d ! F ! d ! " F ! ! d ! d ! d ! " F ! ! d ! " " 30 #" 24 # # 20 " 10 # " 920 foot-pounds (2) Let u ! "\$ 3,1, ! 4 % and v ! "\$ ! 2,2,1 % . Verify the Cauchy-Schwartz inequality and the triangle inequality. u ! ! v ! " ! 6 # 2 ! 4 " ! 8, || u ! || " 3 2 # 1 # " ! 4 # 2 " 26 , || v ! || " " ! 2 # 2 # 2 2 # 1 " 3 u ! # v ! "\$ 1,3, ! 3 % , || u ! # v ! || " 1 # 3 2 # " ! 3 # 2 " 19 The Cauchy-Schwartz inequality: | u ! ! v ! | " 8, || u ! || || v ! || " 26 " 3 # " 15. 29706, | u ! ! v ! | \$ || u ! || || v ! || The triangle inequality: || u ! # v ! || " 19 " 4. 358899, || u ! || # || v ! || " 26 # 3 " 8. 099020, || u ! # v ! || \$ || u ! || # || v ! || (3) Extra points: 61*, 63* (show your work in detail) 61. n ! "\$ sin ! , ! cos ! % , v ! "\$ cos ! ,sin

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Unformatted text preview: ! % , w ! "\$ 0, ! w % . n ! ! v ! " sin ! cos ! ! cos ! sin ! " 0, so n ! and v ! are orthogonal (or perpendicular). 1 || v ! || " cos 2 ! # sin 2 ! " 1, comp v ! w ! " w ! ! v ! || v ! || " ! w sin ! 1 " ! w sin ! || n ! || " sin 2 ! # cos 2 ! " 1, comp n ! w ! " w ! ! n ! || n ! || " w cos ! 1 " w cos ! 63. a ! "\$ ! 100,200 % , b ! "\$ 100,300 % a ! ! b ! " ! 10000 # 60000 " 50000, || a ! || " " ! 100 # 2 # 200 2 " 100 5 , b ! " 100 2 # 300 2 " 100 10 cos ! 1 a ! ! b ! || a ! || b ! " cos ! 1 50000 100 5 100 10 " cos ! 1 1 2 " " 4 2...
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hwsol_3 - w"\$ 0 w n v" sin cos cos sin" 0 so n...

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