Answered: - How do I do number one on this homework set: "Determine the unit

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Answered: - How do I do number one on this homework set: "Determine the unit

How do I do number one on this homework set:

"Determine the unit vector perpinducular to the plane that contains the vectors A = 2x = 6y -3z and B = 4x +3y -z

Physics 110A Problem Set #1

Due Thursday, January 14, 2016

Part I

(Please finish this part by Friday, January 8.)

1. Determine the unit vector perpendicular to the plane that contains the vectors

? ?

A 2 x 6 y 3z and B 4 x 3 y z .

2. The height of a hill is given by h(x, y) x 2 2y 2 xy 7x 7y 2 . Find

(a) The location of the top of the hill.

(b) The height of the hill.

3. Griffiths 1.13.

(Same problem number in 3rd ed.)

4. Calculate the divergence and curl of the following vector:

(a) A ( x 2 yz ) x ( y 2 zx ) y ( z 2 xy) z .

(b) B x3 x 3x 2 z 2 y 3x 2 zz

5. (a) Griffiths 1.22 part (a)

(b) Look at part (b) of prob. 1.22 and predict the answer (and explain of course).

(Note: If you use 3rd ed., the problem# is 1.21)

6. Griffiths 1.32.

(Problem 1.31 in 3rd ed.)

Part II

(Please finish this part by Thursday, January 14.)

7. Check Stokes? theorem using the vector A zx xz over a circular path of radius R in the

xz plane, centered at the origin.

8. Test the divergence theorem for the vector A xyx yzy 3xzz , over the volume of a cube

with edges of length 2 oriented along the positive x, y, and z axes.

9. Griffiths 1.39.

(1.38 in 3rd ed.)

10. Griffiths 1.45.

(1.44 in 3rd ed.)

11. Griffiths 2.3.

(Same problem number in 3rd ed.)

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