

1. 
Find the sum of and . 





A. 

B. 



C. 

D. 



Hint 


2. 
The magnitude of is 41.3 meters and the magnitude of is 53.6 meters. If and are perpendicular, what is the magnitude of their sum? 


A. 
about 41.9 meters 
B. 
about 54.0 meters 


C. 
about 34.2 meters 
D. 
about 67.7 meters 


Hint 


3. 
A vector that has a magnitude of one is called a _____. 


A. 
scalar 
B. 
magnitude 


C. 
unit vector 
D. 
resultant 


Hint 


4. 
Find the magnitude of the vector . 


A. 

B. 



C. 

D. 



Hint 


5. 
Find the inner product of and if and . 


A. 
20 
B. 
12 


C. 
12 
D. 
20 


Hint 


6. 
Find if and . 


A. 

B. 



C. 

D. 



Hint 


7. 
Write an equation in slopeintercept form of the line whose parametric equations are x = 6 + 3t and y = 5  4t. 


A. 

B. 



C. 

D. 



Hint 


8. 
Find the initial horizontal velocity and vertical velocity of a stone kicked with an initial velocity of 15 feet per second at an angle of 42° with the ground. 


A. 
about 11 ft/s, about 10 ft/s 
B. 
about 11 ft/s, about 13 ft/s 


C. 
about 10 ft/s, about 22 ft/s 
D. 
about 14 ft/s, about 12 ft/s 


Hint 


9. 
Which of the following is a dilation matrix? 


A. 

B. 



C. 

D. 



Hint 


10. 
A transformation in threedimensional space is represented by . Which matrix represents this transformation? 


A. 

B. 



C. 

D. 



Hint 


11. 
Find the magnitude of the vector from the origin to point P(7, 5, 23). 


A. 

B. 



C. 

D. 
5 


Hint 


12. 
Write as the sum of unit vectors for U(4, 3, 8) and V(5, 4, 2). 


A. 

B. 



C. 

D. 



Hint 


13. 
In physics, you can determine how much force with which an object is sliding down a frictionless incline by adding the gravitational force vector and the ''normal force'' vector. The normal force vector is always directed up out of the incline perpendicular to it (90° more than the measure of the incline). The magnitude m of the normal force can be calculated by m = f cos , where f is the gravitational force and is the angle measure of the incline. If a gravitational force (always straight down) of 50 N is being exerted on an object on a 25° incline, what is the magnitude of the force with which it is sliding down the incline? 





A. 
45.3 N 
B. 
21.1 N 


C. 
93.1 N 
D. 
50 N 


Hint 


14. 
If José pushes a cart horizontally, exerting a horizontal force of 0.5 N up a 45° incline so that the cart moves 3 m, how much work has José done on the cart? A joule (J) is the SI unit for work or energy. 1 J = 1 N · 1 m 


A. 
J 
B. 
J 


C. 
J 
D. 
J 


Hint 


15. 
Write parametric equations for 2x + 4y = 11. 


A. 
x = 2t  11 and y = 4t  11 


B. 
x = t and y = 


C. 
x = and y = 


D. 
x = t and y = 


Hint 


16. 
Hetu is playing catch with a friend. If Hetu throws the ball at 21.3 m/s, at an angle of 30° with the horizontal, and his friend catches the ball at the same height from which Hetu threw it, how far away is his friend standing? 


A. 
23.1 m 
B. 
46.2 m 


C. 
53.4 m 
D. 
40.0 m 


Hint 

