Math 281                                                                      Name: ___________________

Test #1: Chapter 13                                                      Date  : ___________________

 Directions:  Show all work for full credit. Use only Calculus III techniques to complete problems. No TI-Voyage200, 89, or 92 graphing calculators allowed. You may not use notes, textbooks, or any other reference on this test. Be sure to show all of your supporting work carefully, clearly, and in proper mathematical form. Solutions offered without such supporting work will not receive any credit.

1.       Given the points   and , find the following:

 a)     

 b)     

 c)       

 d)      cosine of the angle between   and

 e)      unit vector in the direction of  

f)      

 g)      a vector orthogonal to the plane containing  and  . Explain the significance of your result.

2.       Find x so that the given vectors are orthogonal:   and .

3.       Find a set of parametric equations for the line of intersection of the two planes x + 4y – 3z = 1 and

-3x + 6y + 7z = 0.

4.       Find an equation for the plane parallel to the plane 2x – 3y + z = 7 and passing through the point .

5.       Find a set of parametric equations for the line containing the points  and .

6.       Find the work done in moving a 20 pound box 50 feet along a conveyor belt inclined at an angle of 30°

Note: Consider gravity to be the only force acting and use a vector approach to solve the problem.

7.       Change from rectangular to spherical coordinates:  .

Graph in three dimensions each of the figures in problems #7-10.  Classify each by naming its shape. Show the equations of several cross sections, and sketch the surface by labeling axes and showing several cross sections and a minimum of two intercepts/vertices/or other important points.

 8.      

9.      

 10.  

 11.     

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