COURSE
MATH 3191: Applied Linear Algebra. 
Fall 1995. University of Colorado at Denver

INSTRUCTOR 
Dr. Andrew Knyazev
Office: CU (Dravo) 620G. Phone: 556-8102.
Office hours: Tue 3pm - 6pm

TEXTBOOK
Elementary Linear Algebra. 7th ed. Howard Anton and Chris Rorres. Wiley, 1994.


Exam #3     (Chapter 3)         Monday, November 20, 1995


______________________________________________________________________________

 
 
 
 
 
           
1. Let u and v be unit vectors, and uv=1. Then the area
of the triange determined by u and v is 
  
[A] 0   [B]    3   [C]  3 /2  [D]  None     

[E] Such vectors do not exist  




2. The dot product of (0, 1, 1) and (1, 2, 0) is

[A]   0   [B]    1   [C]  2   [D]  4     [E]   None



 
3. The cosine  of the angle between vectors (0, 1, 1) and (1, 1, 0) is

[A]   0   [B]    1   [C]  1/2   [D]  1/4     [E]   None




4. The first component of the projection of vector (0, 1, 1) 
on vector (1, 0, 0) is 

[A]   0   [B]    1   [C]  1/2   [D]  1/4     [E]   None




5. Find the area of the triangle determined
by the points (0, 1, 1), (1, 2, 0), and (1, 1, 0):

[A]   0   [B]    1   [C]  1/2   [D]  1/4     [E]   None 






            
6. Find the volume of the parallelepiped determined
by vectors (0, 1, 1), (1, 2, 0), and (1, 1, 0):

[A]   0   [B]    1   [C]  2   [D]  4     [E]   None
 



7. Find the distance between two parallel planes
x+6y+4=0 and x+3y=0

[A]   2   [B]    3   [C]   4   [D]   None    

[E] The planes are not parallel   




8. Find the equation of the plane passing through the points
(0, 1, 1), (1, 2, 0), and (1, 1, 0):

[A] x+3y=0   [B] z=0   [C] x+y-2=0    [D] x+y-3=0   [E]   None 




9. Find the equation of the line passing through the points
(1, 1, 1) and (1, 1, 0):

[A] x=y=0   [B] z=0   [C] x+y-2=0    [D] x=t, y=t, z=t   [E]   None 




10. Find the distance between the point (5, 5, 5) and the plane
3x+4y-8=0:

[A] -1   [B] 0   [C] 1   [D] 2  [E]   None