Question 1

Convert  from rectangular to cylindrical coordinates.

Accepted Answer

A)   
B)   
C)   
D)   
E)    C

Question 2

Find  .

Accepted Answer

A)   
B)   
C)   
D)   
E)    B

Question 3

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

Accepted Answer

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

Question 4

Suppose  . Find the vector in the same direction as u with twice the length of u.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 5

Find the distance from the sphere  to the point (0, 0, 11).

Accepted Answer

The answer of Find the distance from the sphere ...

Question 6

Find the point where the line which passes through (1, 8, 2) and is parallel to  intersects the xy-plane.

Accepted Answer

The answer of Find the point where the line which...

Question 7

Let  . Find the length of u.

Accepted Answer

The answer of Let  . Find the length of...

Question 8

If  , then find

Accepted Answer

The answer of If  , then find ...

Question 9

Find the direction vector for the line joining the points  and  .

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 10

The equation for a cylinder with radius 5 oriented symmetrically about the y-axis is

Accepted Answer

The answer of The equation for a cylinder with radius...

Question 11

Find the norm of v.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 12

Let  . Find the vector x that satisfies  .

Accepted Answer

A)   
B)   
C)   
D)   
E)

Question 13

A rectangular box has a corner at the origin and corners at (0, 0, 4), (0, 7, 0), (9, 0, 0), (4, 7, 0), (4, 0, 9), and (0, 7, 9). The other corner is

Accepted Answer

The answer of A rectangular box has a corner at...

Question 14

Identify the quadratic surface defined by  .

Accepted Answer

A)   Ellipsoid
B)   Elliptic cone
C)   Elliptic paraboloid
D)   Hyperbolic paraboloid
E)   Sphere

Question 15

Find

Accepted Answer

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B)    
B)     
C)     
D)     
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C)    
B)     
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D)     
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D)    
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E)    
B)     
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D)     
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Question 16

Identify the quadratic surface defined by  .

Accepted Answer

A)   Ellipsoid
B)   Elliptic cone
C)   Elliptic paraboloid
D)   Hyperbolic paraboloid
E)   Sphere

Question 17

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

Accepted Answer

The answer of Complete the square to identify the center...

Question 18

If  , then find

Accepted Answer

The answer of If  , then find ...

Question 19

Find the orthogonal projection of the vector  in the direction of the vector  .

Accepted Answer

The answer of Find the orthogonal projection of the vector...

Question 20

Convert  from spherical to rectangular coordinates.

Accepted Answer

A)   
B)   
C)   
D)   
E)

Exam 11: Three-Dimensional Space; Vectors

Convert from rectangular to cylindrical coordinates.

Find .

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

Suppose . Find the vector in the same direction as u with twice the length of u.

Find the distance from the sphere to the point (0, 0, 11).

Find the point where the line which passes through (1, 8, 2) and is parallel to intersects the xy-plane.

Let . Find the length of u.

If , then find

Find the direction vector for the line joining the points and .

The equation for a cylinder with radius 5 oriented symmetrically about the y-axis is

Find the norm of v.

Let . Find the vector x that satisfies .

A rectangular box has a corner at the origin and corners at (0, 0, 4), (0, 7, 0), (9, 0, 0), (4, 7, 0), (4, 0, 9), and (0, 7, 9). The other corner is

Identify the quadratic surface defined by .

Find

Identify the quadratic surface defined by .

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

If , then find

Find the orthogonal projection of the vector in the direction of the vector .

Convert from spherical to rectangular coordinates.