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Unformatted text preview: A = -x ^ + 7 y ^ + 6 z ^ and B = -x ^ 6 y ^ + 6 z ^ . 6. Find the curl and divergence of the vector A = x x ^ xy y ^ + 3z 2 z ^ . 7. Sketch the vector field A = -y x ^ + x y ^ and calculate its curl. 8. (a) Prove that the two-dimensional rotation matrix (1.29) preserves dot products. That is, show that A y B y + A z B z = A _ y B _ y +A _ z B _ z . (b) What constraints must the elements R ij of the three-dimensional rotation matrix (1.30) satisfy in order to preserve the length of A for all vectors A ....
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This note was uploaded on 02/20/2012 for the course PHYS 1101 taught by Professor Lowellwood during the Fall '10 term at University of Houston.
- Fall '10