Question 1

Compute -4a - 5b.

Accepted Answer

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

Question 2

Find a vector perpendicular to the given vector. Show all your work.

Accepted Answer

Answer may vary. Fin

Question 3

Find two unit vectors parallel to the given vector. From   to

Accepted Answer

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

Question 4

Use geometry to identify the cross product.

Accepted Answer

A)  -4j 
B)  0 
C)  4i 
D)  4k 
A)  -4j 
B)  0 
C)  4i 
D)  4k

Question 5

Match the equation to its graph. [The figures below are not necessarily drawn to scale.]

Accepted Answer

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

Question 6

Find symmetric equations of the line through   and   .

Accepted Answer

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

Question 7

Compute   .

Accepted Answer

A)    
B)  -25 
C)    
D)  643 
A)    
B)  -25 
C)    
D)  643

Question 8

A small communications satellite is being maneuvered by two on-board thrusters. One thruster generates a force with magnitude 12 newtons in a direction   . In response to the applied thrusts, the satellite moves under a total force of   (the components are in units of newtons). Find the thrust vector for the second thruster.

Accepted Answer

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

Question 9

Identify the surface.

Accepted Answer

A)  elliptic paraboloid 
B)  cone 
C)  ellipsoid 
D)  hyperbolic paraboloid 
A)  elliptic paraboloid 
B)  cone 
C)  ellipsoid 
D)  hyperbolic paraboloid

Question 10

Determine whether the vectors a and b are parallel.

Accepted Answer

A)  parallel 
B)  not parallel 
A)  parallel 
B)  not parallel

Question 11

Find a unit vector in the same direction as the given vector. 10i - 2j

Accepted Answer

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

Question 12

Find the distance between the given points. (5, -7, 7), (7, 7, 7)

Accepted Answer

A)    
B)  200 
C)    
D)  340 
A)    
B)  200 
C)    
D)  340

Question 13

Use the cross product to determine the angle between the vectors, assuming that   . Round to the nearest thousandth.

Accepted Answer

A)  1.571 
B)  0.149 
C)  0.396 
D)  1.175 
A)  1.571 
B)  0.149 
C)  0.396 
D)  1.175

Question 14

Find the indicated area. Area of the triangle with vertices   ,   , and

Accepted Answer

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

Question 15

Find symmetric equations of the line through   and normal to the plane   .

Accepted Answer

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

Question 16

Match the equation to its graph. [The figures below are not necessarily drawn to scale.]

Accepted Answer

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

Question 17

Compute the angle between the vectors. Round your answer to two decimal places.

Accepted Answer

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

Question 18

In many farmers' barns and in many mechanics' shops, you can find a stout steel pipe about 2 to 3 feet in length with one end pinched so that the pinched end fits snugly over a wrench handle. What might explain the common presence of this object in these settings? Explain your answer in terms of the vector concepts you have learned.

Accepted Answer

Answers may vary.
The purpose

Question 19

Find a vector with the given magnitude and in the same direction as the given vector. Magnitude 6,

Accepted Answer

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

Question 20

Match the equation to its graph. [The figures below are not necessarily drawn to scale.]

Accepted Answer

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

Compute -4a - 5b.

Find a vector perpendicular to the given vector. Show all your work.

Find two unit vectors parallel to the given vector. From to

Use geometry to identify the cross product.

Match the equation to its graph. [The figures below are not necessarily drawn to scale.]

Find symmetric equations of the line through and .

Compute .

Identify the surface.

Determine whether the vectors a and b are parallel.

Find a unit vector in the same direction as the given vector. 10i - 2j

Find the distance between the given points. (5, -7, 7), (7, 7, 7)

Use the cross product to determine the angle between the vectors, assuming that . Round to the nearest thousandth.

Find the indicated area. Area of the triangle with vertices , , and

Find symmetric equations of the line through and normal to the plane .

Match the equation to its graph. [The figures below are not necessarily drawn to scale.]

Compute the angle between the vectors. Round your answer to two decimal places.

Find a vector with the given magnitude and in the same direction as the given vector. Magnitude 6,

Match the equation to its graph. [The figures below are not necessarily drawn to scale.]

Preliminaries

Limits and Continuity

Differentiation

Applications of the Derivative

Integration

Applications of the Definite Integral

Exponentials, Logarithms and Other Transcendental Functions

Integration Techniques

First-Order Differential Equations

Infinite Series

Parametric Equations and Polar Coordinates

Vector-Valued Functions

Functions of Several Variables and Partial Differentiation

Multiple Integrals

Vector Calculus

Second Order Differential Equations

Filters

Exam 12: Vectors and the Geometry of Space

Compute -4a - 5b.

Find a vector perpendicular to the given vector. Show all your work.

Find two unit vectors parallel to the given vector. From to

Use geometry to identify the cross product.

Match the equation to its graph. [The figures below are not necessarily drawn to scale.]

Find symmetric equations of the line through and .

Compute .

Identify the surface.

Determine whether the vectors a and b are parallel.

Find a unit vector in the same direction as the given vector. 10i - 2j

Find the distance between the given points. (5, -7, 7), (7, 7, 7)

Use the cross product to determine the angle between the vectors, assuming that . Round to the nearest thousandth.

Find the indicated area. Area of the triangle with vertices , , and

Find symmetric equations of the line through and normal to the plane .

Match the equation to its graph. [The figures below are not necessarily drawn to scale.]

Compute the angle between the vectors. Round your answer to two decimal places.

Find a vector with the given magnitude and in the same direction as the given vector. Magnitude 6,

Match the equation to its graph. [The figures below are not necessarily drawn to scale.]

Preliminaries

Limits and Continuity

Differentiation

Applications of the Derivative

Integration

Applications of the Definite Integral

Exponentials, Logarithms and Other Transcendental Functions

Integration Techniques

First-Order Differential Equations

Infinite Series

Parametric Equations and Polar Coordinates

Vector-Valued Functions

Functions of Several Variables and Partial Differentiation

Multiple Integrals

Vector Calculus

Second Order Differential Equations

Filters