ECE3025_F05_Exam_Solutions

# ECE3025_F05_Exam_Solutions - ECE 3025C Electromagnetics...

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ECE 3025C -- Electromagnetics EXAM #2 Solutions October 25, 2005 Page 1 of 4 Problem 1. (25 points) Three vectors in a rectangular coordinate system are given by 23 = +− JG ±± ± XY Z Aa aa , 32 =+ ±±± XYZ Ba a a , and 3 =− + Caaa . Answer the following: A. Find the vector + AB (5 points) . () ( ) 21 33 12 3 6 3 += + ++ +−− = + − ± ± ± ± Z X Y Z a a a a a a B. Find the vector ABC (5 points) ( ) 2 3 6 3 9 2 1 6 2 1 4 9 +−= + + + + + = + ± ± ± ± Z X Y Z a a a a a a C. Find the vector x x (5 points) ( ) {} n Since not specified, here are the answers for both ( x ) x and x ( x ) ( x ) x 2 3 -1 x 6 3 + 1 4 + 6 3 x 3 3 3 x 13 - 2 ( ⎧⎫ ⎪⎪ == + + = + + ⎨⎬ ⎩⎭ J G J GJ G J G J G ± ± ± J Z X Y Z AB C A BC aaa AB C C a a a C a a a A ()()() ()( )( ) { } x ) x -3 3 3 3 3 + 9 3 + 3 9 6 12 6 3- 1 - 1 ) x 1 3 -2 3 2 + 6 1 + 1 9 7 10 11 ) + + = + = = G J G ± ± ± ±±±± ± ± X Y Z X Y Z BC a a a a a a CA A a a a A a a a C 2 3 -1 30 7 + 1 20 + 14 3 37 19 17 1- 7 - 1 0 =− − −+ − − + ± ± ± Z X Y Z a a a

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October 25, 2005 2 ECE 3025C Exam #2 Problem 1. (Continued) D. Find a unit vector normal to the plane defined by the endpoints of vectors and , , J GJ G J G AB C (10 points) () ( ) ( ) ( ) ( ) ( ) ()( )() 12 33 21 1 , 0 ,1 32 13 11 4 2 1 ,4 , 2 Normal to Plane ABC x 1 0 1 0 4 1 2 4 0 14 2 −= =− +− + −+ = −− = − − + ++ = − + =− ⎧⎫ ⎪⎪ == = =− + + ⎨⎬ ⎩⎭ JG JJJG ±± ± ± ± ± ± ± ± ±±± XY Z X
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ECE3025_F05_Exam_Solutions - ECE 3025C Electromagnetics...

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