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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

 


 


 

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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.

 

(c) The maximum slope of the hill at x = 3, y = 2, and its direction.

 


 

3. Griffiths 1.13.

 

(Same problem number in 3rd ed.)

 

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

 


 

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

 


 

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

 

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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.)

 


 

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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.

 


 


 

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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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