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?
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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?
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10. Write
the equation
a.
Using cylindrical coordinates.
b.
Using spherical coordinates.
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