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Solution to Quiz1

# Solution to Quiz1 - ENEE 380 Fall 2011 Discussion Quiz 1 2...

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ENEE 380 Fall 2011 2 September 2011 Discussion Quiz 1 Note: This is an assessment test on vector calculus. It is not a graded quiz. Answer as many problems as you can. 1. Find the angle between the body diagonals of a cube. (Hint: Determine the vectors corresponding to the face diagonals and use the vector dot product.) 2. Check the fundamental theorem for gradient, using 2 3 4 2 T x xy yz , the points 0,0,0 a , 1,1,1 b , and the path 0,0,0 1,0,0 1,1,0 1,1,1 .     T d T T b a l b a a) Calculate T . b) Calculate T d b a l using the given path. c) Calculate     T T a b and compare your result with part b). 3. Test the divergence theorem using the vector field, ˆ ˆ ˆ v xy 2xy 3zx x y z . Take as your volume a cube with sides of length 2.

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