Chapter 11/12 Practice Test



1.
Find the vector v whose initial and terminal points are given below.

(2,3), (6,7)


 
A.
B.
C.
D.
E.


2.
Find the unit vector in the direction of u.



The possible solutions are given to two decimal places.
A.
            
B.
C.
D.
E.


3.
Given the vectors



find the following:

 
(a)
(b)      
(c)
     
A.
     1
         0
 
B.
     1
         1
 
C.
     0
         1
 
D.
     1
         1
 
E.
     1
         0
 


4.
Find the component form of vector v given its magnitude and the angle it makes with the positive x-axis.





     
A.
B.
C.
D.
E.


5.
Find the component form of the vector u with the given initial and terminal points.

Initial point:      (2 , 8 , 4 )

Terminal point: (–4 , 4 , 1 )
A.
B.
C.
D.
E.


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

               

                     
A.
–44.44 degrees
B.
168.69 degrees
C.
91.38 degrees
D.
–78.69 degrees
E.
None of the above


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

               

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


8.
Given the vectors u and v, find and .

               
 
A.
 
B.
 
 
C.
 
 
D.
 
 
E.
 
 


9.
Find the area of a parallelogram that has the given vectors as adjacent sides.

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


10.
Use the triple scalar product to find the volume of the parallelepiped having adjacent edges given by the vectors

       
A.
B.
C.
D.
E.


11.
Find || r(t)|| given the function r(t) below.

A.
         
B.
C.
D.
E.


12.
The position vector r describes the path of an object moving in space. Find the velocity, speed, and acceleration of the object.


Velocity
Speed
Acceleration
 
A.
0
            
B.
 
C.
 
D.
 
E.
 


13.
The position vector r describes the path of an object moving in the xy-plane. Find the velocity and acceleration vectors at the given value of t.

A.
            
B.
C.
D.
E.


14.
Use the given acceleration function to find the velocity and position vector. Then find the position at time t = 2.

A.
         
B.
C.
D.
E.



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