ProblemSet5_Solutions - 70 , 4 ) | ( . 02 , 5 . 70 , 4 ) |...

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ECE 3025 Problem Set #5 (1) Problem 13.17 from Hayt/Buck (2) Problem 13.1 from Hayt/Buck (3) Problem 16.2 at the end of Lecture Note #14 (4) Problem 1.15 from Hayt/Buck (5) Problem 1.18 from Hayt/Buck
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ECE3025B Problem Set #1 Solutions 1.15. Three vectors extending from the origin are given as r 1 = ( 7 , 3 , 2 ) , r 2 = ( 2 , 7 , 3 ) , and r 3 = ( 0 , 2 , 3 ) . Find: a) a unit vector perpendicular to both r 1 and r 2 : a p 12 = r 1 × r 2 | r 1 × r 2 | = ( 5 , 25 , 55 ) 60 . 6 = ( 0 . 08 , 0 . 41 , 0 . 91 ) b) a unit vector perpendicular to the vectors r 1 r 2 and r 2 r 3 : r 1 r 2 = ( 9 , 4 , 1 ) and r 2 r 3 = ( 2 , 5 , 6 ) .So r 1 r 2 × r 2 r 3 = ( 19 , 52 , 32 ) . Then a p = ( 19 , 52 , 32 ) | ( 19 , 52 , 32 ) | = ( 19 , 52 , 32 ) 63 . 95 = ( 0 . 30 , 0 . 81 , 0 . 50 ) c) the area of the triangle defined by r 1 and r 2 : Area = 1 2 | r 1 × r 2 |= 30 . 3 d) the area of the triangle defined by the heads of r 1 , r 2 , and r 3 : Area = 1 2 | ( r 2 r 1 ) × ( r 2 r 3 ) |= 1 2 | ( 9 , 4 , 1 ) × ( 2 , 5 , 6 ) |= 32 . 0 1.18. Given points A(ρ = 5 = 70 ,z =− 3 ) and B(ρ = 2 =− 30 ,z = 1 ) , find: a) unit vector in cartesian coordinates at A toward B : A( 5 cos 70 , 5 sin 70 , 3 ) = A( 1 . 71 , 4 . 70 , 3 ) , In the same manner, B( 1 . 73 , 1 , 1 ) .So R AB = ( 1 . 73 , 1 , 1 ) ( 1 . 71 , 4 . 70 , 3 ) = ( 0 . 02 , 5 . 70 , 4 ) and therefore a AB = ( 0 . 02 , 5 .
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Unformatted text preview: 70 , 4 ) | ( . 02 , 5 . 70 , 4 ) | = ( . 003 , . 82 , . 57 ) b) a vector in cylindrical coordinates at A directed toward B : a AB a = . 003 cos 70 . 82 sin 70 = . 77. a AB a = . 003 sin 70 . 82 cos 70 = . 28. Thus a AB = . 77 a . 28 a + . 57 a z . c) a unit vector in cylindrical coordinates at B directed toward A : Use a BA = ( , 003 , . 82 , . 57 ) . Then a BA a = . 003 cos ( 30 ) + . 82 sin ( 30 ) = . 43, and a BA a = . 003 sin ( 30 ) + . 82 cos ( 30 ) = . 71. Finally, a BA = . 43 a + . 71 a . 57 a z 1...
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This note was uploaded on 03/15/2010 for the course ECE 3025 taught by Professor Citrin during the Spring '08 term at Georgia Institute of Technology.

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ProblemSet5_Solutions - 70 , 4 ) | ( . 02 , 5 . 70 , 4 ) |...

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