Question 1

Find the direction cosines of the vector u given below.

Accepted Answer

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C)    
D)    
E)    
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E)

Question 2

Convert the following point from cylindrical coordinates to rectangular coordinates.

Accepted Answer

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B)    
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D)    
E)    
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D)    
E)

Question 3

Find an equation in cylindrical coordinates for the equation given in rectangular coordinates.

Accepted Answer

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E)

Question 4

Suppose a car is towed using a force of 1300 newtons. The chain used to pull the car makes a   angle with the horizontal. Find the work done in towing the car 3 kilometers. Round your answer to two decimal places.

Accepted Answer

A)  7,070.20 km-N 
B)  3,534.60 km-N 
C)  3,549.60 km-N 
D)  7,068.20 km-N 
E)  1,648.21 km-N 
A)  7,070.20 km-N 
B)  3,534.60 km-N 
C)  3,549.60 km-N 
D)  7,068.20 km-N 
E)  1,648.21 km-N

Question 5

Complete the square to write the following equation in the standard form for a sphere. ​   ​

Accepted Answer

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

Question 6

Find an equation in spherical coordinates for the equation given in rectangular coordinates. ​   ​

Accepted Answer

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

Question 7

Find an equation for the surface of revolution generated by revolving the curve   in the yz-plane about the y-axis.

Accepted Answer

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Question 8

Find the unit vector in the direction of u.

Accepted Answer

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D)    
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Question 9

Find the distance between the point   and the line given by the set of parametric equations   . ​

Accepted Answer

A)    /3 ​ 
B)  1
​ 
C)    /3 ​ 
D)  3
​ 
E)    ​/1 
A)    /3 ​ 
B)  1
​ 
C)    /3 ​ 
D)  3
​ 
E)    ​/1

Question 10

Use the triple scalar product to find the volume of the parallelepiped having adjacent edges given by the vectors ​   ​

Accepted Answer

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

Find the direction cosines of the vector u given below.

Convert the following point from cylindrical coordinates to rectangular coordinates.

Find an equation in cylindrical coordinates for the equation given in rectangular coordinates.

Suppose a car is towed using a force of 1300 newtons. The chain used to pull the car makes a angle with the horizontal. Find the work done in towing the car 3 kilometers. Round your answer to two decimal places.

Complete the square to write the following equation in the standard form for a sphere.

Find an equation in spherical coordinates for the equation given in rectangular coordinates.

Find an equation for the surface of revolution generated by revolving the curve in the yz-plane about the y-axis.

Find the unit vector in the direction of u.

Find the distance between the point and the line given by the set of parametric equations .

Use the triple scalar product to find the volume of the parallelepiped having adjacent edges given by the vectors

Preparation for Calculus

Limits and Their Properties

Differentiation

Applications of Differentiation

Integration

Differential Equations

Applications of Integration

Integration Techniques and Improper Integrals

Infinite Series

Conics, Parametric Equations, and Polar Coordinates

Vector-Valued Functions

Functions of Several Variables

Multiple Integration

Vector Anal

Filters

Exam 11: Vectors and the Geometry of Space

Find the direction cosines of the vector u given below.

Convert the following point from cylindrical coordinates to rectangular coordinates.

Find an equation in cylindrical coordinates for the equation given in rectangular coordinates.

Suppose a car is towed using a force of 1300 newtons. The chain used to pull the car makes a angle with the horizontal. Find the work done in towing the car 3 kilometers. Round your answer to two decimal places.

Complete the square to write the following equation in the standard form for a sphere. ​ ​

Find an equation in spherical coordinates for the equation given in rectangular coordinates. ​ ​

Find an equation for the surface of revolution generated by revolving the curve in the yz-plane about the y-axis.

Find the unit vector in the direction of u.

Find the distance between the point and the line given by the set of parametric equations . ​

Use the triple scalar product to find the volume of the parallelepiped having adjacent edges given by the vectors ​ ​

Preparation for Calculus

Limits and Their Properties

Differentiation

Applications of Differentiation

Integration

Differential Equations

Applications of Integration

Integration Techniques and Improper Integrals

Infinite Series

Conics, Parametric Equations, and Polar Coordinates

Vector-Valued Functions

Functions of Several Variables

Multiple Integration

Vector Anal

Filters

Complete the square to write the following equation in the standard form for a sphere.

Find an equation in spherical coordinates for the equation given in rectangular coordinates.

Find the distance between the point and the line given by the set of parametric equations .

Use the triple scalar product to find the volume of the parallelepiped having adjacent edges given by the vectors