Question 1

Consider the cylinder in   
a. Identify the coordinate axis to which the cylinder is parallel. 
b. Sketch the cylinder.
-y =

Accepted Answer

A)  a. Parallel to y-axis; b.
   
B)  a. Parallel to x-axis; b. 
  
C)  a. Parallel to x-axis; b. 
  
D)  a. Parallel to x-axis; b. 
  
A)  a. Parallel to y-axis; b.
   
B)  a. Parallel to x-axis; b. 
  
C)  a. Parallel to x-axis; b. 
  
D)  a. Parallel to x-axis; b.

Question 2

Express the vector in the form ai + bj.
-  if A is the point ( -1, -7) and B is the point ( 4, -14)

Accepted Answer

A)  v = 5i + 7j 
B)  v = 5i - 7j 
C)  v = -5i + 7j 
D)  v = 7i - 5j 
A)  v = 5i + 7j 
B)  v = 5i - 7j 
C)  v = -5i + 7j 
D)  v = 7i - 5j

Question 3

Determine whether the following is always true or not always true. Given reasons for your answers.
-(u × v) ∙ v = 0

Accepted Answer

Always tru

Question 4

Find the angle between u and v in radians.
-u = 9i + 4j + 7k, v = 9i + 2j + 8k

Accepted Answer

A)  1.39 
B)  1.06 
C)  1.49 
D)  0.18 
A)  1.39 
B)  1.06 
C)  1.49 
D)  0.18

Question 5

Find the indicated vector.
-Let u =   , v =   . Find v - u.

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 6

Solve the problem.
-Find the area of the triangle determined by the points P(-3, 6, -4), Q( 10, -1, -2), and

Accepted Answer

A)    
B)    
C)    
D)  3   
A)    
B)    
C)    
D)  3

Question 7

Determine whether the following is always true or not always true. Given reasons for your answers.
-|u| =

Accepted Answer

Always tru

Question 8

Express the vector in the form ai + bj + ck.
-2u - 6v if u =   and v =

Accepted Answer

A)  v = 2i + 2j - 6k 
B)  v = -16i + 8j - 6k 
C)  v = 20i + 2j - 6k 
D)  v = -16i + 2j - 6k 
A)  v = 2i + 2j - 6k 
B)  v = -16i + 8j - 6k 
C)  v = 20i + 2j - 6k 
D)  v = -16i + 2j - 6k

Question 9

Identify the type of surface represented by the given equation.
-  +   -   = 1

Accepted Answer

A)  Elliptical cone 
B)  Hyperboloid of two sheets 
C)  Hyperboloid of one sheet 
D)  Ellipsoid 
A)  Elliptical cone 
B)  Hyperboloid of two sheets 
C)  Hyperboloid of one sheet 
D)  Ellipsoid

Question 10

Solve the problem.
-A bird flies from its nest 2 km in the direction 39° north of east, where it stops to rest on a tree. It then flies 5 km in the direction 13° south of west and lands atop a telephone pole. With an xy-coordinate system where the origin is the bird's nest, the x-axis points east, and the y-axis points north, at what point is the tree located?

Accepted Answer

A)  ( 1.259, 1.554) 
B)  ( 1.554, 1.259) 
C)  ( 0.5333, 1.928) 
D)  ( 0.7771, 0.6293) 
A)  ( 1.259, 1.554) 
B)  ( 1.554, 1.259) 
C)  ( 0.5333, 1.928) 
D)  ( 0.7771, 0.6293)

Question 11

Write the word or phrase that best completes each statement or answers the question. 
-The unit vectors u and v are combined to produce two new vectors   and   Show that a and b are orthogonal. Assume

Accepted Answer

The answer of Write the word or phrase that best...

Question 12

Find a parametrization for the line segment beginning at   and ending at   .
-  ( -2, -2, -2) and

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 13

Write the equation for the plane.
-The plane through the point P( 5, 5, 7) and parallel to the plane

Accepted Answer

A)  4y = -31 
B)  -8x - 8y + 7z = 31 
C)  -8x - 8y + 7z = -31 
D)  -8x - 8y + 7z = 129 
A)  4y = -31 
B)  -8x - 8y + 7z = 31 
C)  -8x - 8y + 7z = -31 
D)  -8x - 8y + 7z = 129

Question 14

Find the magnitude of u × v and the unit vector parallel to u × v in the direction of u × v.
-u = 4i + 2j + 8k, v = -i - 2j - 2k

Accepted Answer

A)  180;   i +   k 
B)  6   ;   i +   k 
C)  180;   i +   j +   k 
D)  6   ;   i -   k 
A)  180;   i +   k 
B)  6   ;   i +   k 
C)  180;   i +   j +   k 
D)  6   ;   i -   k

Question 15

Determine whether the following is always true or not always true. Given reasons for your answers.
-(u × v) . w = u . (w × v)

Accepted Answer

Not always true; (u × v) ? w =

Question 16

Find parametric equations for the line described below.
-The line through the points P(-1, -1, 7) and Q( -7, 4, 3)

Accepted Answer

A)  x = -6t - 1, y = 5t - 1, z = -4t + 7 
B)  x = t - 6, y = t + 5, z = 7t - 4 
C)  x = t + 6, y = t - 5, z = 7t + 4 
D)  x = -6t + 1, y = 5t + 1, z = -4t - 7 
A)  x = -6t - 1, y = 5t - 1, z = -4t + 7 
B)  x = t - 6, y = t + 5, z = 7t - 4 
C)  x = t + 6, y = t - 5, z = 7t + 4 
D)  x = -6t + 1, y = 5t + 1, z = -4t - 7

Question 17

Find an equation for the sphere with the given center and radius.
-Center (0, 0, 5), radius = 10

Accepted Answer

A)  
  
B)  
  
C)  
  
D)  
  
A)  
  
B)  
  
C)  
  
D)

Question 18

Match the equation with the surface it defines.    
-  +   = 16

Accepted Answer

A)  Figure 1 
B)  Figure 4 
C)  Figure 2 
D)  Figure 3 
A)  Figure 1 
B)  Figure 4 
C)  Figure 2 
D)  Figure 3

Question 19

Find the angle between u and v in radians.
-u = 8i, v = 7i - 9j

Accepted Answer

A)  0.91 
B)  0.66 
C)  1.28 
D)  1.56 
A)  0.91 
B)  0.66 
C)  1.28 
D)  1.56

Question 20

Identify the type of surface represented by the given equation.
-  -   -   = 1

Accepted Answer

A)  Ellipsoid 
B)  Hyperboloid of one sheet 
C)  Hyperboloid of two sheets 
D)  Elliptical cone 
A)  Ellipsoid 
B)  Hyperboloid of one sheet 
C)  Hyperboloid of two sheets 
D)  Elliptical cone

Consider the cylinder in a. Identify the coordinate axis to which the cylinder is parallel. b. Sketch the cylinder. -y =

Express the vector in the form ai + bj. - if A is the point ( -1, -7) and B is the point ( 4, -14)

Determine whether the following is always true or not always true. Given reasons for your answers. -(u × v) ∙ v = 0

Find the angle between u and v in radians. -u = 9i + 4j + 7k, v = 9i + 2j + 8k

Find the indicated vector. -Let u = , v = . Find v - u.

Solve the problem. -Find the area of the triangle determined by the points P(-3, 6, -4), Q( 10, -1, -2), and

Determine whether the following is always true or not always true. Given reasons for your answers. -|u| =

Express the vector in the form ai + bj + ck. -2u - 6v if u = and v =

Identify the type of surface represented by the given equation. - + - = 1

Write the word or phrase that best completes each statement or answers the question. -The unit vectors u and v are combined to produce two new vectors and Show that a and b are orthogonal. Assume

Find a parametrization for the line segment beginning at and ending at . - ( -2, -2, -2) and

Write the equation for the plane. -The plane through the point P( 5, 5, 7) and parallel to the plane

Find the magnitude of u × v and the unit vector parallel to u × v in the direction of u × v. -u = 4i + 2j + 8k, v = -i - 2j - 2k

Determine whether the following is always true or not always true. Given reasons for your answers. -(u × v) . w = u . (w × v)

Find parametric equations for the line described below. -The line through the points P(-1, -1, 7) and Q( -7, 4, 3)

Find an equation for the sphere with the given center and radius. -Center (0, 0, 5), radius = 10

Match the equation with the surface it defines. - + = 16

Find the angle between u and v in radians. -u = 8i, v = 7i - 9j

Identify the type of surface represented by the given equation. - - - = 1

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Exam 13: Vectors and the Geometry of Space