Math 2A  Chapter 9 Test  Fall ’07  Name:___________________

Show your work for credit.  No calculators are needed.

1.      Let .  Find two unit vectors parallel to .

2.      What work is done by the force vector  in moving an object from the origin to (2,3,4)?  Assume the force is measured in Newtons and the distances are measured in meters.

3.      Find the angle between the vectors  and  where the coordinates
are  , and  .

4.      Find the distance between the plane  and the plane .

5.      Find an equation for the plane S containing the x-axis and passing through the point P(1, 2, 3) .

6.      Consider the quadric surface  described by the equation  

a.       Write the equation in standard form

b.      Identify the surface as one of the following: a hyperbolic paraboloid, an elliptical cone, an elliptical paraboloid, an ellipsoid, a hyperboloid of one sheet or a hyperboloid of two sheets. 

c.       What is the intersection of the surface with the plane x = 2?

7.      Find the magnitude of the torque vector at P if a 20 Newton force is applied to the rigid body shown in the diagram at right. Note that this is a planar diagram.   Recall that  where  is the lever arm vector  is the force vector and θ is the angle between them.

8.      Describe the cross section that the given plane makes with the surface  

a.       z = 9

b.      x =2y

9.      The spherical coordinates of a point are  

a.    What are the rectangular coordinates?

b.    What are the cylindrical coordinates?

 

10.  Write the equation  

a.       Using cylindrical coordinates.

b.      Using spherical coordinates.