Question 1

If   , find   .

Accepted Answer

The answer of If   , find  ...

Question 2

If

Accepted Answer

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

Question 3

If

Accepted Answer

The answer of If  ...

Question 4

Identify the trace of the surface defined by   when   .

Accepted Answer

A)  Circle 
B)  Ellipse 
C)  Parabola 
D)  Hyperbola 
E)  Line 
A)  Circle 
B)  Ellipse 
C)  Parabola 
D)  Hyperbola 
E)  Line

Question 5

Find the parametric equations for the line passing through   and   .

Accepted Answer

The answer of Find the parametric equations for the line...

Question 6

Identify the trace of the surface   when

Accepted Answer

The answer of Identify the trace of the surface ...

Question 7

Are   ,   , and   coplanar?

Accepted Answer

The answer of Are   ,   ,...

Question 8

The equation of a surface is given in rectangular coordinates. Give the equation of the surface in cylindrical coordinates.

Accepted Answer

The answer of The equation of a surface is given...

Question 9

Convert   from cylindrical to rectangular coordinates.

Accepted Answer

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

Question 10

The spherical surface   is centered at

Accepted Answer

A)  (0, 0, 0) 
B)  (1, 1, 1) 
C)  (-2, -3, 1) 
D)    
E)  (-2, -2, -2) 
A)  (0, 0, 0) 
B)  (1, 1, 1) 
C)  (-2, -3, 1) 
D)    
E)  (-2, -2, -2)

Question 11

Identify the quadratic surface defined by   .

Accepted Answer

The answer of Identify the quadratic surface defined by ...

Question 12

Find the equation of the sphere with a diameter whose endpoints are   and   .

Accepted Answer

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

Question 13

Find the parametric equations for the line passing through   and   .

Accepted Answer

The answer of Find the parametric equations for the line...

Question 14

Find the components of the vector   if   .

Accepted Answer

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

Question 15

Convert   from cylindrical to rectangular coordinates.

Accepted Answer

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

Question 16

Find   .

Accepted Answer

A)    
B)    
C)    
D)  0 =   
E)    
A)    
B)    
C)    
D)  0 =   
E)

Question 17

Find the parametric equations for the line whose vector form is given by   .

Accepted Answer

A)    
B)    
C)    
D)    , z = 1 
E)    
A)    
B)    
C)    
D)    , z = 1 
E)

Question 18

Identify the trace of the surface defined by   when   .

Accepted Answer

A)  Circle 
B)  Ellipse 
C)  Parabola 
D)  Hyperbola 
E)  Line 
A)  Circle 
B)  Ellipse 
C)  Parabola 
D)  Hyperbola 
E)  Line

Question 19

Find the scalar triple product for the vectors   ,   , and   .

Accepted Answer

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

Question 20

Find the dot product   .

Accepted Answer

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

If , find .

If

If

Identify the trace of the surface defined by when .

Find the parametric equations for the line passing through and .

Identify the trace of the surface when

Are , , and coplanar?

The equation of a surface is given in rectangular coordinates. Give the equation of the surface in cylindrical coordinates.

Convert from cylindrical to rectangular coordinates.

The spherical surface is centered at

Identify the quadratic surface defined by .

Find the equation of the sphere with a diameter whose endpoints are and .

Find the parametric equations for the line passing through and .

Find the components of the vector if .

Convert from cylindrical to rectangular coordinates.

Find .

Find the parametric equations for the line whose vector form is given by .

Identify the trace of the surface defined by when .

Find the scalar triple product for the vectors , , and .

Find the dot product .

Limits and Continuity

The Derivative

Topics in Deifferentiation

The Derivative in Graphing and Applications

Integration

Applications of the Definite Integral in Geometry, Science and Engineering

Principle of Integral Evaluation

Mathematical Modeling With Differential Equations

Infinte Series

Parametric and Polar Curves; Conic Sections

Vector-Valued Functions

Partial Derivatives

Multiple Integrals

Topics in Vector Calculus

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Exam 11: Three-Dimensional Space; Vectors

If , find .

If

If

Identify the trace of the surface defined by when .

Find the parametric equations for the line passing through and .

Identify the trace of the surface when

Are , , and coplanar?

The equation of a surface is given in rectangular coordinates. Give the equation of the surface in cylindrical coordinates.

Convert from cylindrical to rectangular coordinates.

The spherical surface is centered at

Identify the quadratic surface defined by .

Find the equation of the sphere with a diameter whose endpoints are and .

Find the parametric equations for the line passing through and .

Find the components of the vector if .

Convert from cylindrical to rectangular coordinates.

Find .

Find the parametric equations for the line whose vector form is given by .

Identify the trace of the surface defined by when .

Find the scalar triple product for the vectors , , and .

Find the dot product .

Limits and Continuity

The Derivative

Topics in Deifferentiation

The Derivative in Graphing and Applications

Integration

Applications of the Definite Integral in Geometry, Science and Engineering

Principle of Integral Evaluation

Mathematical Modeling With Differential Equations

Infinte Series

Parametric and Polar Curves; Conic Sections

Vector-Valued Functions

Partial Derivatives

Multiple Integrals

Topics in Vector Calculus

Filters