Question 1

Find the direction cosines of a vector perpendicular to   .

Accepted Answer

The answer of Find the direction cosines of a vector...

Question 2

If   ,   , and   , find   and   .

Accepted Answer

The answer of If   ,   ,...

Question 3

Find the point of intersection of the two lines L1:
 
   and L2:

Accepted Answer

Question 4

The distance from (6, 8, 11) to the yz-plane is

Accepted Answer

A)  6 
B)  8 
C)  11 
D)  14.866069 
E)  10 
A)  6 
B)  8 
C)  11 
D)  14.866069 
E)  10

Question 5

Find   .

Accepted Answer

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

Question 6

The distance from (2, -1, -4) to the xy-plane is

Accepted Answer

The answer of The distance from (2, -1, -4) to...

Question 7

Complete the square to identify the center and radius of the following sphere:

Accepted Answer

It is a sp

Question 8

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

Accepted Answer

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

Question 9

Find the vector equation of the line joining the points   and   .

Accepted Answer

A)   
  ,
  
B)    ,

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

C)    ,
  ,
  
D)    ,
  ,
  
E)    ,
  ,

Question 10

Find the angle between   and   .

Accepted Answer

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

Question 11

Find the vector equation of the line given the parametric form is   ,   , and   .

Accepted Answer

A)   
  ,
  
B)    ,

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

C)    ,
  ,
  
D)    ,
  ,
  
E)    ,
  ,

Question 12

Find the cosine of the angle between   and   .

Accepted Answer

The answer of Find the cosine of the angle between...

Question 13

Find the equation of the plane that passes through the point   and has   as a normal.

Accepted Answer

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

Find the direction cosines of a vector perpendicular to .

If , , and , find and .

Find the point of intersection of the two lines L_1: and L₂:

The distance from (6, 8, 11) to the yz-plane is

Find .

The distance from (2, -1, -4) to the xy-plane is

Complete the square to identify the center and radius of the following sphere:

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

Find the vector equation of the line joining the points and .

Find the angle between and .

Find the vector equation of the line given the parametric form is , , and .

Find the cosine of the angle between and .

Find the equation of the plane that passes through the point and has as a normal.

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

Find the direction cosines of a vector perpendicular to .

If , , and , find and .

Find the point of intersection of the two lines L1: and L2:

The distance from (6, 8, 11) to the yz-plane is

Find .

The distance from (2, -1, -4) to the xy-plane is

Complete the square to identify the center and radius of the following sphere:

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

Find the vector equation of the line joining the points and .

Find the angle between and .

Find the vector equation of the line given the parametric form is , , and .

Find the cosine of the angle between and .

Find the equation of the plane that passes through the point and has as a normal.

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

Find the point of intersection of the two lines L_1: and L₂: