Question 1

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

Accepted Answer

Question 2

If   , find

Accepted Answer

A)  627 
B)  -627 
C)  891 
D)  -891 
E)  0 
A)  627 
B)  -627 
C)  891 
D)  -891 
E)  0

Question 3

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

Accepted Answer

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

Question 4

Convert   from rectangular to cylindrical coordinates.

Accepted Answer

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

Question 5

Lines   and   are

Accepted Answer

A)  intersecting at one point 
B)  skew 
C)  parallel 
D)  perpendicular 
E)  the same line 
A)  intersecting at one point 
B)  skew 
C)  parallel 
D)  perpendicular 
E)  the same line

Question 6

If

Accepted Answer

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

Question 7

Convert (4,   ,   ) from spherical to rectangular coordinates.

Accepted Answer

A)  (4, 4, 4) 
B)  (0, 4, 0) 
C)  (0, 0, 4) 
D)  (4, 0, 0) 
E)  (0, 0, 0) 
A)  (4, 4, 4) 
B)  (0, 4, 0) 
C)  (0, 0, 4) 
D)  (4, 0, 0) 
E)  (0, 0, 0)

Question 8

Find the approximate distance between the point   and   .

Accepted Answer

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

Question 9

Convert   from rectangular to spherical coordinates.

Accepted Answer

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

Question 10

Identify the quadratic surface defined by   .

Accepted Answer

A)  Ellipsoid 
B)  Elliptic cone 
C)  Elliptic paraboloid 
D)  Hyperbolic paraboloid 
E)  Not a surface 
A)  Ellipsoid 
B)  Elliptic cone 
C)  Elliptic paraboloid 
D)  Hyperbolic paraboloid 
E)  Not a surface

Question 11

Identify the quadratic surface defined by   .

Accepted Answer

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

Question 12

Convert   from spherical to cylindrical coordinates.

Accepted Answer

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

Question 13

Lines   and   are

Accepted Answer

A)  intersecting at one point 
B)  skew 
C)  parallel 
D)  perpendicular 
E)  the same line 
A)  intersecting at one point 
B)  skew 
C)  parallel 
D)  perpendicular 
E)  the same line

Question 14

Find a unit vector in the direction of   .

Accepted Answer

The answer of Find a unit vector in the direction...

Question 15

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

Accepted Answer

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

Question 16

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

Accepted Answer

The answer of Find an equation of the plane that...

Question 17

Convert   from rectangular to spherical coordinates.

Accepted Answer

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

Question 18

Find the angle between   and   .

Accepted Answer

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

Question 19

Find the equation of the plane through (5, 5, 11) and perpendicular to

Accepted Answer

The answer of Find the equation of the plane through...

Question 20

The distance from the sphere   to the point (0, 0, 5) is

Accepted Answer

A)  5 
B)  4 
C)  0 
D)  9 
E)  1 
A)  5 
B)  4 
C)  0 
D)  9 
E)  1

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

If , find

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

Convert from rectangular to cylindrical coordinates.

Lines and are

If

Convert (4, , ) from spherical to rectangular coordinates.

Find the approximate distance between the point and .

Convert from rectangular to spherical coordinates.

Identify the quadratic surface defined by .

Identify the quadratic surface defined by .

Convert from spherical to cylindrical coordinates.

Lines and are

Find a unit vector in the direction of .

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

Find an equation of the plane that passes through <4, 5, 9> and has the vector as a normal vector.

Convert from rectangular to spherical coordinates.

Find the angle between and .

Find the equation of the plane through (5, 5, 11) and perpendicular to

The distance from the sphere to the point (0, 0, 5) is

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

Exam 11: Three-Dimensional Space; Vectors

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

If , find

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

Convert from rectangular to cylindrical coordinates.

Lines and are

If

Convert (4, , ) from spherical to rectangular coordinates.

Find the approximate distance between the point and .

Convert from rectangular to spherical coordinates.

Identify the quadratic surface defined by .

Identify the quadratic surface defined by .

Convert from spherical to cylindrical coordinates.

Lines and are

Find a unit vector in the direction of .

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

Find an equation of the plane that passes through <4, 5, 9> and has the vector as a normal vector.

Convert from rectangular to spherical coordinates.

Find the angle between and .

Find the equation of the plane through (5, 5, 11) and perpendicular to

The distance from the sphere to the point (0, 0, 5) is

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: