Question 1

Write the equation for the plane.
-The plane through the point P( 4, -5, 6) and parallel to the plane

Accepted Answer

A)  4x - 5y + 6z = 52 
B)  6x + 4y + 8z = 52 
C)  6x + 4y + 8z = -52 
D)  4x + 8y + 6z = 52 
A)  4x - 5y + 6z = 52 
B)  6x + 4y + 8z = 52 
C)  6x + 4y + 8z = -52 
D)  4x + 8y + 6z = 52 B

Question 2

Solve the problem.
-How much work does it take to slide a box 37 meters along the ground by pulling it with a 213 N force at an angle of 30° from the horizontal?

Accepted Answer

A)  3940.5   joules 
B)  7881   joules 
C)    joules 
D)  7881 joules 
A)  3940.5   joules 
B)  7881   joules 
C)    joules 
D)  7881 joules A

Question 3

Find the magnitude of u × v and the unit vector parallel to u × v in the direction of u × v.
-u = -3i - 8i + 5k, v = 0

Accepted Answer

A)  0; no direction 
B)  0; -3i - 8i + 5k 
C)  7   ;   ( -3i - 8i + 5k) 
D)  0;   ( -3i - 8i + 5k) 
A)  0; no direction 
B)  0; -3i - 8i + 5k 
C)  7   ;   ( -3i - 8i + 5k) 
D)  0;   ( -3i - 8i + 5k) A

Question 4

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

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 5

Consider the cylinder in   
a. Identify the coordinate axis to which the cylinder is parallel. 
b. Sketch the cylinder.
-x -   = 0

Accepted Answer

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

Question 6

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

Accepted Answer

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

Question 7

Find the indicated vector.
-Let u =   . Find 2u.

Accepted Answer

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

Question 8

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

Accepted Answer

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

Question 9

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

Accepted Answer

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

Question 10

Find the triple scalar product (u x v) ∙ w of the given vectors.
-u = 4i + 2j - k; v = 6i + 6j - 4k; w = 1i + 8j - 4k

Accepted Answer

A)  70 
B)  -50 
C)  -222 
D)  30 
A)  70 
B)  -50 
C)  -222 
D)  30

Question 11

Find the magnitude of u × v and the unit vector parallel to u × v in the direction of u × v.
-u = 4i, v = 3j

Accepted Answer

A)  4; 3k 
B)  12; -k 
C)  12; 12k 
D)  12; k 
A)  4; 3k 
B)  12; -k 
C)  12; 12k 
D)  12; k

Question 12

Write the word or phrase that best completes each statement or answers the question. 
-Show that the midpoint of the hypotenuse of a right triangle is equidistant from all three vertices. [Hint: See the figure below. Show that   =   .]

Accepted Answer

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

Question 13

Find a parametrization for the line segment beginning at   and ending at   .
-  (0, 0, 0) and   ( 4, 3, -4)

Accepted Answer

A)  x = 4t, y = 3t, z = -4t 
B)  x = -4t, y = -3t, z = 4t 
C)  x = 4t + 4, y = 3t + 3, z = -4t - 4 
D)  x = 4t - 4, y = 3t - 3, z = -4t + 4 
A)  x = 4t, y = 3t, z = -4t 
B)  x = -4t, y = -3t, z = 4t 
C)  x = 4t + 4, y = 3t + 3, z = -4t - 4 
D)  x = 4t - 4, y = 3t - 3, z = -4t + 4

Question 14

Find the intersection.
-x + y + z = 7, x + y = 12

Accepted Answer

A) x = t, y = 12 - t, z = -5 
B)  x = -t, y = 12 + t, z = -5 
C)  x = -t, y = 12 + t, z = 5 
D)  x = -1, y = 1 + 12t, z = -5t 
A) x = t, y = 12 - t, z = -5 
B)  x = -t, y = 12 + t, z = -5 
C)  x = -t, y = 12 + t, z = 5 
D)  x = -1, y = 1 + 12t, z = -5t

Question 15

Identify the type of surface represented by the given equation.
-  +   = 6

Accepted Answer

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

Question 16

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

Accepted Answer

A)  Paraboloid 
B)  Elliptical cone 
C)  Sphere 
D)  Ellipsoid 
A)  Paraboloid 
B)  Elliptical cone 
C)  Sphere 
D)  Ellipsoid

Question 17

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

Accepted Answer

A)  
  
B)  
  
C)  
  
D)  0 
A)  
  
B)  
  
C)  
  
D)  0

Question 18

Use a calculator to find the acute angle between the planes to the nearest thousandth of a radian.
-4x - 4y + 9z = -10 and -5x - 3y + 7z = 10

Accepted Answer

A)  0.967 rad 
B)  1.478 rad 
C)  0.604 rad 
D)  0.196 rad 
A)  0.967 rad 
B)  1.478 rad 
C)  0.604 rad 
D)  0.196 rad

Question 19

Find the angle between u and v in radians.
-u = 4i - 9j - 6k, v = 5i + 5j - 5k

Accepted Answer

A)  1.57 
B)  1.55 
C)  0.05 
D)  1.52 
A)  1.57 
B)  1.55 
C)  0.05 
D)  1.52

Question 20

Find v ∙ u.
-v = 8i - 7j and u = -4i - 5j

Accepted Answer

A)  4i - 12j 
B)  3 
C)  -67 
D)  -32i + 35j 
A)  4i - 12j 
B)  3 
C)  -67 
D)  -32i + 35j

Write the equation for the plane. -The plane through the point P( 4, -5, 6) and parallel to the plane

Solve the problem. -How much work does it take to slide a box 37 meters along the ground by pulling it with a 213 N force at an angle of 30° from the horizontal?

Find the magnitude of u × v and the unit vector parallel to u × v in the direction of u × v. -u = -3i - 8i + 5k, v = 0

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

Consider the cylinder in a. Identify the coordinate axis to which the cylinder is parallel. b. Sketch the cylinder. -x - = 0

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

Find the indicated vector. -Let u = . Find 2u.

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

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

Find the triple scalar product (u x v) ∙ w of the given vectors. -u = 4i + 2j - k; v = 6i + 6j - 4k; w = 1i + 8j - 4k

Find the magnitude of u × v and the unit vector parallel to u × v in the direction of u × v. -u = 4i, v = 3j

Write the word or phrase that best completes each statement or answers the question. -Show that the midpoint of the hypotenuse of a right triangle is equidistant from all three vertices. [Hint: See the figure below. Show that = .]

Find a parametrization for the line segment beginning at and ending at . - (0, 0, 0) and ( 4, 3, -4)

Find the intersection. -x + y + z = 7, x + y = 12

Identify the type of surface represented by the given equation. - + = 6

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

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

Use a calculator to find the acute angle between the planes to the nearest thousandth of a radian. -4x - 4y + 9z = -10 and -5x - 3y + 7z = 10

Find the angle between u and v in radians. -u = 4i - 9j - 6k, v = 5i + 5j - 5k

Find v ∙ u. -v = 8i - 7j and u = -4i - 5j

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

Write the equation for the plane. -The plane through the point P( 4, -5, 6) and parallel to the plane

Solve the problem. -How much work does it take to slide a box 37 meters along the ground by pulling it with a 213 N force at an angle of 30° from the horizontal?

Find the magnitude of u × v and the unit vector parallel to u × v in the direction of u × v. -u = -3i - 8i + 5k, v = 0

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

Consider the cylinder in a. Identify the coordinate axis to which the cylinder is parallel. b. Sketch the cylinder. -x - = 0

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

Find the indicated vector. -Let u = . Find 2u.

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

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

Find the triple scalar product (u x v) ∙ w of the given vectors. -u = 4i + 2j - k; v = 6i + 6j - 4k; w = 1i + 8j - 4k

Find the magnitude of u × v and the unit vector parallel to u × v in the direction of u × v. -u = 4i, v = 3j

Write the word or phrase that best completes each statement or answers the question. -Show that the midpoint of the hypotenuse of a right triangle is equidistant from all three vertices. [Hint: See the figure below. Show that = .]

Find a parametrization for the line segment beginning at and ending at . - (0, 0, 0) and ( 4, 3, -4)

Find the intersection. -x + y + z = 7, x + y = 12

Identify the type of surface represented by the given equation. - + = 6

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

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

Use a calculator to find the acute angle between the planes to the nearest thousandth of a radian. -4x - 4y + 9z = -10 and -5x - 3y + 7z = 10

Find the angle between u and v in radians. -u = 4i - 9j - 6k, v = 5i + 5j - 5k

Find v ∙ u. -v = 8i - 7j and u = -4i - 5j

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