Question 1

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

Accepted Answer

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

Question 2

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

Accepted Answer

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

Question 3

Determine whether the pairs of lines are parallel, intersect at a single point, or are skew. If the lines are parallel, determine whether they are the same line (and thus intersect at all points). If the lines intersect at a single point, determine the point of intersection.
-x = 1 + 3t, y = 3 - 3t, z = -t and x = 3 + 4s, y = -1 - 2s, z = 3 - 5s

Accepted Answer

A)  The lines are skew. 
B)  The lines are parallel, distinct lines. 
C)  The lines intersect at a single point, (7, -3, -2). 
D)  The lines intersect at a single point, (-5, 1, 3). 
A)  The lines are skew. 
B)  The lines are parallel, distinct lines. 
C)  The lines intersect at a single point, (7, -3, -2). 
D)  The lines intersect at a single point, (-5, 1, 3).

Question 4

Solve the problem.
-Let u = -2i + 8j, v = 2i + 3j, and w = i - j. Write u =   +   where   is parallel to v and   is parallel to w.

Accepted Answer

A)    = 3v 
  = 2w 
B)    = -4 v 
  = -24 w 
C)    = 1.200 v 
  = -4.400 w 
D)    = 0.8333 v 
  = - 0.2273 w 
A)    = 3v 
  = 2w 
B)    = -4 v 
  = -24 w 
C)    = 1.200 v 
  = -4.400 w 
D)    = 0.8333 v 
  = - 0.2273 w

Question 5

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

Accepted Answer

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

Question 6

Write the equation for the plane.
-The plane through the points P( -1, 8, -58) , Q( 2, -2, 27) and

Accepted Answer

A) 5x + 7y + z = -3 
B)  5x - 7y - z = -3 
C)  5x - 7y - z = 3 
D)  5x + 7y +z = 3 
A) 5x + 7y + z = -3 
B)  5x - 7y - z = -3 
C)  5x - 7y - z = 3 
D)  5x + 7y +z = 3

Question 7

Find u.   
-v = i + j + k, u = 12i + 3j + 4k

Accepted Answer

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

Question 8

Find a parametrization for the line segment beginning at   and ending at   .
-  ( -4, 0, -5) and   (0, -2, 0)

Accepted Answer

A)  x = 5t - 4, y = 3t, z = 6t - 5, 0 $\le$ t $\le$1 
B)  x = 5t, y = 3t - 2, z = 6t, 0 $\le$ t $\le$ 1 
C)  x = 4t - 4, y = -2t, z = 5t - 5, 0 $\le$ t $\le$ 1 
D)  x = -4t, y = 2t - 2, z = -5t, 0 $\le$ t $\le$ 1 
A)  x = 5t - 4, y = 3t, z = 6t - 5, 0 $\le$ t $\le$1 
B)  x = 5t, y = 3t - 2, z = 6t, 0 $\le$ t $\le$ 1 
C)  x = 4t - 4, y = -2t, z = 5t - 5, 0 $\le$ t $\le$ 1 
D)  x = -4t, y = 2t - 2, z = -5t, 0 $\le$ t $\le$ 1

Question 9

Find the magnitude of u × v and the unit vector parallel to u × v in the direction of u × v.
-u = 7i + 5j , v = i - j

Accepted Answer

A)  2; 2k 
B)  2; -2k 
C)  12; -k 
D)  12; -12k 
A)  2; 2k 
B)  2; -2k 
C)  12; -k 
D)  12; -12k

Question 10

Find both the parametric and the vector equation of the line.
-The line through (0, 1, 0) in the direction of the vector v = (3, 0, -1)

Accepted Answer

A)  x = 3, y = t, z = -1; r = (3, 0, -1) + t(0, 1, 0) 
B)  x = 3, y = t, z = -1; r = (0, 1, 0) + t(3, 0, -1) 
C)  x = 3t, y = 1, z = -t; r = (3, 0, -1) + t(0, 1, 0) 
D)  x = 3t, y = 1, z = -t; r = (0, 1, 0) + t(3, 0, -1) 
A)  x = 3, y = t, z = -1; r = (3, 0, -1) + t(0, 1, 0) 
B)  x = 3, y = t, z = -1; r = (0, 1, 0) + t(3, 0, -1) 
C)  x = 3t, y = 1, z = -t; r = (3, 0, -1) + t(0, 1, 0) 
D)  x = 3t, y = 1, z = -t; r = (0, 1, 0) + t(3, 0, -1)

Question 11

Solve the problem.
-Find the work done by a force of 9i (newtons) in moving as object along a line from the origin to the point   (distance in meters).

Accepted Answer

A)  38.18 joules 
B)  54   joules 
C)  9   joules 
D)  54 joules 
A)  38.18 joules 
B)  54   joules 
C)  9   joules 
D)  54 joules

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

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

Solve the problem. -Let u = -2i + 8j, v = 2i + 3j, and w = i - j. Write u = + where is parallel to v and is parallel to w.

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

Write the equation for the plane. -The plane through the points P( -1, 8, -58) , Q( 2, -2, 27) and

Find u. -v = i + j + k, u = 12i + 3j + 4k

Find a parametrization for the line segment beginning at and ending at . - ( -4, 0, -5) and (0, -2, 0)

Find the magnitude of u × v and the unit vector parallel to u × v in the direction of u × v. -u = 7i + 5j , v = i - j

Find both the parametric and the vector equation of the line. -The line through (0, 1, 0) in the direction of the vector v = (3, 0, -1)

Solve the problem. -Find the work done by a force of 9i (newtons) in moving as object along a line from the origin to the point (distance in meters).

Functions

Limits

Derivatives

Applications of the Derivative

Integration

Applications of Integration

Logarithmic, Exponential, and Hyperbolic Functions

Integration Techniques

Differential Equations

Sequences and Infinite Series

Power Series

Parametric and Polar Curves

Vector-Valued Functions

Functions of Several Variables

Multiple Integration

Vector Calculus

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Exam 13: Vectors and the Geometry of Space

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

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

Solve the problem. -Let u = -2i + 8j, v = 2i + 3j, and w = i - j. Write u = + where is parallel to v and is parallel to w.

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

Write the equation for the plane. -The plane through the points P( -1, 8, -58) , Q( 2, -2, 27) and

Find u. -v = i + j + k, u = 12i + 3j + 4k

Find a parametrization for the line segment beginning at and ending at . - ( -4, 0, -5) and (0, -2, 0)

Find the magnitude of u × v and the unit vector parallel to u × v in the direction of u × v. -u = 7i + 5j , v = i - j

Find both the parametric and the vector equation of the line. -The line through (0, 1, 0) in the direction of the vector v = (3, 0, -1)

Solve the problem. -Find the work done by a force of 9i (newtons) in moving as object along a line from the origin to the point (distance in meters).

Functions

Limits

Derivatives

Applications of the Derivative

Integration

Applications of Integration

Logarithmic, Exponential, and Hyperbolic Functions

Integration Techniques

Differential Equations

Sequences and Infinite Series

Power Series

Parametric and Polar Curves

Vector-Valued Functions

Functions of Several Variables

Multiple Integration

Vector Calculus

Filters