AP Calculus BC - Chapter 11 Practice Test
Name: __________________________ Date: _____________
Chapter 11 Practice Test



1.
Find vectors u and v whose initial and terminal points are given. Determine whether u and v are equivalent.

u:      (6,7), (9,9)           v: (2,–3), (5,–1)



 
A.
, , which are equivalent.
B.
, , which are equivalent.
C.
, , which are equivalent.
D.
, , which are equivalent.
E.
, , which are not equivalent.


2.
Find the magnitude of the vector given below.

A.
            
B.
C.
D.
E.


3.
Three forces with magnitudes 90 pounds, 120 pounds and 45 pounds act on an object at angles , , and , respectively, with the positive x-axis. Find the direction and magnitude of the resultant force.

(The choices below are given to two decimal places.)
     
A.
with the positive x-axis.
B.
with the positive x-axis.
C.
with the positive x-axis.
D.
with the positive x-axis.
E.
with the positive x-axis.


4.
Find the standard equation of the sphere with center (2 , 7, –5 ), and radius 5 .

A.
B.
C.
D.
E.


5.
Find the unit vector in the direction of u.

A.
B.
C.
D.
E.


6.
Find the angle between the vectors for u and v given below.

               

                     
A.
41.81 degrees
B.
26.57 degrees
C.
84.26 degrees
D.
63.43 degrees
E.
None of the above


7.
Determine whether u and v are orthogonal, parallel, or neither.

               

                     
A.
Parallel, opposite direction
B.
Neither parallel nor orthogonal
C.
Parallel, same direction
D.
Orthogonal
E.
None of the above


8.
Find the direction cosines of the vector u given below.

               

                     
A.
B.
C.
D.
E.


9.
Find the projection of u onto v, and the vector component of u orthogonal to v.


               

Projection of u onto v
Component of u orthogonal to v
                 
A.
 
B.
 
 
C.
 
 
D.
 
 
E.
 
 


10.
Work   An object is pulled 10 feet across a floor, using a force of 100 pounds. The direction of the force is 35 above the horizontal.

Find the work done.
               

                     
A.
15.77 ft-lbs
B.
819.15 ft-lbs
C.
573.58 ft-lbs
D.
903.69 ft-lbs
E.
None of the above


11.
Given the vectors u and v, find and .

               
 
A.
 
B.
 
 
C.
 
 
D.
 
 
E.
 
 


12.
Find the area of a parallelogram that has the given vectors as adjacent sides.

               
A.
B.
C.
D.
E.
None of the above


13.
Use the triple scalar product to find the volume of the parallelepiped having adjacent edges given by the vectors

       
A.
B.
C.
D.
E.


14.
Find a set of parametric equations of the line through the point parallel to the vector v=(8, 4,4).


         
A.
B.
C.
D.
E.


15.
Find an equation of a plane passing through the points



and perpendicular to the plane

.



         
A.
B.
C.
D.
E.


16.
Determine whether the following planes are parallel, orthogonal, or neither. If they are neither parallel nor orthogonal, find the angle of intersection.





         
A.
The planes are parallel.
B.
The planes are orthogonal.
C.
The planes are neither parallel nor orthogonal, the angle of intersection is .
D.
The planes are neither parallel nor orthogonal, the angle of intersection is .
E.
None of the above


17.
Find the distance between the point (3, –2, 3) and the plane given below.






         
A.
B.
C.
D.
E.


18.
Find the distance between the planes given below.




   
A.
B.
C.
D.
E.


19.
Identify the following quadric surface.




         
A.
Ellipsoid
B.
Hyperboloid of one sheet
C.
Hyperboloid of two sheets
D.
Elliptic cone
E.
Elliptic paraboloid
F.
Hyperbolic paraboloid


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