Question 1

Find u.   
-v = 7i - 3j + k, u = -3j + 4k

Accepted Answer

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

Question 2

Identify the type of surface represented by the given equation.
-  +   = 5

Accepted Answer

A)  Parabolic cylinder 
B)  Ellipsoid 
C)  Elliptical cylinder 
D)  Paraboloid 
A)  Parabolic cylinder 
B)  Ellipsoid 
C)  Elliptical cylinder 
D)  Paraboloid

Question 3

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

Accepted Answer

Always tru

Question 4

Give a geometric description of the set of points whose coordinates satisfy the given conditions.
-  +   +   < 1

Accepted Answer

A)  All points outside the lower hemisphere centered at ( 1, 7, 3) 
B)  All points on the lower hemisphere centered at ( 1, 7, 3) 
C)  No set of points satisfy the given relations. 
D)  All points within the lower hemisphere centered at ( 1, 7, 3) 
A)  All points outside the lower hemisphere centered at ( 1, 7, 3) 
B)  All points on the lower hemisphere centered at ( 1, 7, 3) 
C)  No set of points satisfy the given relations. 
D)  All points within the lower hemisphere centered at ( 1, 7, 3)

Question 5

Find the indicated vector.
-Let u =   , v =   . Find -u + 2v.

Accepted Answer

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

Question 6

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

Accepted Answer

A)  Ellipsoid 
B)  Elliptical cone 
C)  Paraboloid 
D)  Hyperbolic paraboloid 
A)  Ellipsoid 
B)  Elliptical cone 
C)  Paraboloid 
D)  Hyperbolic paraboloid

Question 7

Find the angle between u and v in radians.
-u = 7j - 2k, v = 4i - 6j - 7k

Accepted Answer

A)  -0.39 
B)  1.75 
C)  1.96 
D)  1.58 
A)  -0.39 
B)  1.75 
C)  1.96 
D)  1.58

Question 8

Solve the problem.
-An airplane is flying in the direction 10° east of south at 701 km/hr. Find the component form of the velocity of the airplane, assuming that the positive x-axis represents due east and the positive y-axis represents due north.

Accepted Answer

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

Question 9

Write the word or phrase that best completes each statement or answers the question. 
-Show that the vectors   b +   a and   b -   a are orthogonal.

Accepted Answer

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

Question 10

Find a parametrization for the line segment beginning at   and ending at   .
-  ( -3, 7, 3) and   (0, 7, 7)

Accepted Answer

A)  x = 3t - 3, y = 7, z = 4t + 3, 0 $\le$ t $\le$ 1 
B)  x = -3t, y = 7t, z = -4t + 7, 0 $\le$ t $\le$ 1 
C)  x = 3t - 3, y = 7t, z = 4t + 3, 0 $\le$t $\le$ 1 
D)  x = -3t, y = 7, z = -4t + 7, 0 $\le$ t $\le$ 1 
A)  x = 3t - 3, y = 7, z = 4t + 3, 0 $\le$ t $\le$ 1 
B)  x = -3t, y = 7t, z = -4t + 7, 0 $\le$ t $\le$ 1 
C)  x = 3t - 3, y = 7t, z = 4t + 3, 0 $\le$t $\le$ 1 
D)  x = -3t, y = 7, z = -4t + 7, 0 $\le$ t $\le$ 1

Question 11

Solve the problem.
-Find the magnitude of the torque in foot-pounds at point P for the following lever:

Accepted Answer

A)  6.34 ft-lb 
B)  3.78 ft-lb 
C)  50 ft-lb 
D)  1.76 ft-lb 
A)  6.34 ft-lb 
B)  3.78 ft-lb 
C)  50 ft-lb 
D)  1.76 ft-lb

Question 12

Match the equation with the surface it defines.    
-  +   +   = 1

Accepted Answer

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

Question 13

Find the indicated vector.
-Let u =   . Find 8u.

Accepted Answer

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

Question 14

Find both the parametric and the vector equation of the line.
-The line through (4, -1, 3) that is perpendicular to both u = (2, 0, -1) and the y-axis.

Accepted Answer

A)  x = 2 - 4t, y = -t, z = -1 + 3t; r = (2, 0, -1) + t(-4, -1, 3) 
B)  x = 4 - t, y = -t, z = 3 + 2t; r = (4, -1, 3) + t(-1, 0, 2) 
C)  x = 4 - 2t, y = -1, z = 3 - t; r = (4, -1, 3) + t(-2, 0, -1) 
D)  x = 4 - t, y = -1, z = 3 + 2t; r = (4, -1, 3) + t(-1, 0, 2) 
A)  x = 2 - 4t, y = -t, z = -1 + 3t; r = (2, 0, -1) + t(-4, -1, 3) 
B)  x = 4 - t, y = -t, z = 3 + 2t; r = (4, -1, 3) + t(-1, 0, 2) 
C)  x = 4 - 2t, y = -1, z = 3 - t; r = (4, -1, 3) + t(-2, 0, -1) 
D)  x = 4 - t, y = -1, z = 3 + 2t; r = (4, -1, 3) + t(-1, 0, 2)

Question 15

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

Accepted Answer

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

Question 16

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

Accepted Answer

Always tru

Question 17

Write the equation for the plane.
-The plane through the point P( 4, -3, 2) and normal to n =   .

Accepted Answer

A)  -2x - 7y - 6z = -1 
B)  4x - 3y + 2z = -1 
C)  2x + 7y + 6z = -1 
D)  -4x + 3y - 2z = -1 
A)  -2x - 7y - 6z = -1 
B)  4x - 3y + 2z = -1 
C)  2x + 7y + 6z = -1 
D)  -4x + 3y - 2z = -1

Question 18

Solve the problem.
-A force of magnitude 8 pounds pulling on a suitcase makes an angle of 30° with the ground. Express the force in terms of its i and j components.

Accepted Answer

A)  6.928i + 4.000 j 
B)  4.000i + 6.928j 
C)  1.234i - 7.904j 
D)  0.8660i + + 0.5000j 
A)  6.928i + 4.000 j 
B)  4.000i + 6.928j 
C)  1.234i - 7.904j 
D)  0.8660i + + 0.5000j

Question 19

Find the triple scalar product (u x v) ∙ w of the given vectors.
-u = -5i - 3j + 4k; v = 5i - 4j + 2k; w = 10i - 5j - 8k

Accepted Answer

A)  -330 
B)  -3 
C)  -410 
D)  30 
A)  -330 
B)  -3 
C)  -410 
D)  30

Question 20

Solve the problem.
-Find the area of the parallelogram determined by the points P(7, -5, 5), Q( 2, -7, -3),   and

Accepted Answer

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

Find u. -v = 7i - 3j + k, u = -3j + 4k

Identify the type of surface represented by the given equation. - + = 5

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

Give a geometric description of the set of points whose coordinates satisfy the given conditions. - + + < 1

Find the indicated vector. -Let u = , v = . Find -u + 2v.

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

Find the angle between u and v in radians. -u = 7j - 2k, v = 4i - 6j - 7k

Solve the problem. -An airplane is flying in the direction 10° east of south at 701 km/hr. Find the component form of the velocity of the airplane, assuming that the positive x-axis represents due east and the positive y-axis represents due north.

Write the word or phrase that best completes each statement or answers the question. -Show that the vectors b + a and b - a are orthogonal.

Find a parametrization for the line segment beginning at and ending at . - ( -3, 7, 3) and (0, 7, 7)

Solve the problem. -Find the magnitude of the torque in foot-pounds at point P for the following lever:

Match the equation with the surface it defines. - + + = 1

Find the indicated vector. -Let u = . Find 8u.

Find both the parametric and the vector equation of the line. -The line through (4, -1, 3) that is perpendicular to both u = (2, 0, -1) and the y-axis.

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

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

Write the equation for the plane. -The plane through the point P( 4, -3, 2) and normal to n = .

Solve the problem. -A force of magnitude 8 pounds pulling on a suitcase makes an angle of 30° with the ground. Express the force in terms of its i and j components.

Find the triple scalar product (u x v) ∙ w of the given vectors. -u = -5i - 3j + 4k; v = 5i - 4j + 2k; w = 10i - 5j - 8k

Solve the problem. -Find the area of the parallelogram determined by the points P(7, -5, 5), Q( 2, -7, -3), and

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

Exam 13: Vectors and the Geometry of Space

Find u. -v = 7i - 3j + k, u = -3j + 4k

Identify the type of surface represented by the given equation. - + = 5

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

Give a geometric description of the set of points whose coordinates satisfy the given conditions. - + + < 1

Find the indicated vector. -Let u = , v = . Find -u + 2v.

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

Find the angle between u and v in radians. -u = 7j - 2k, v = 4i - 6j - 7k

Solve the problem. -An airplane is flying in the direction 10° east of south at 701 km/hr. Find the component form of the velocity of the airplane, assuming that the positive x-axis represents due east and the positive y-axis represents due north.

Write the word or phrase that best completes each statement or answers the question. -Show that the vectors b + a and b - a are orthogonal.

Find a parametrization for the line segment beginning at and ending at . - ( -3, 7, 3) and (0, 7, 7)

Solve the problem. -Find the magnitude of the torque in foot-pounds at point P for the following lever:

Match the equation with the surface it defines. - + + = 1

Find the indicated vector. -Let u = . Find 8u.

Find both the parametric and the vector equation of the line. -The line through (4, -1, 3) that is perpendicular to both u = (2, 0, -1) and the y-axis.

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

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

Write the equation for the plane. -The plane through the point P( 4, -3, 2) and normal to n = .

Solve the problem. -A force of magnitude 8 pounds pulling on a suitcase makes an angle of 30° with the ground. Express the force in terms of its i and j components.

Find the triple scalar product (u x v) ∙ w of the given vectors. -u = -5i - 3j + 4k; v = 5i - 4j + 2k; w = 10i - 5j - 8k

Solve the problem. -Find the area of the parallelogram determined by the points P(7, -5, 5), Q( 2, -7, -3), and

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