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Unformatted text preview: HW-1 1. For the two vectors A x 2 y z and B 2 x 3 y z , find (a) A B and A B , (b) component of B along A , (c) angle between A and B , (d) A B , (e) A B A B . 2. A , B , and C are three vectors pointing from the origin of a coordinate to three points A, B,
and C, respectively. Find the distance between the origin to the ABC plane and the area of the ABC triangle. Express your result in terms of A , B , and C vecotrs.
3. Find the angle between the surface normal directions of r 2=9 and x+y+z2=1 at the joined
point of (2,-2,1).
4. Calculate the divergence and the curl of the following functions: (a) va x 2 x 3xz 2 y 2 xzz . (b) vb xyx 2 yzy 3zxz . (c) vc y 2 x (2 xy z 2 ) y 2 yzz .
5. Calculate the Laplacian of the following functions:
(a) Ta x 2 2 xy 3z 4 .
(b) Tb sin x sin y sin z .
(c) Tc e 5 x sin(4 y) cos(3z) . (d) v x 2 x 3xz 2 y 2 xzz .
6. Prove that the divergence of a curl is always zero and that the curl of a gradient is always
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This note was uploaded on 02/06/2010 for the course PHYSICS 11 taught by Professor Qiu during the Fall '09 term at Berkeley.
- Fall '09