Question 1

Determine if the vectors are orthogonal.

Accepted Answer

A)  orthogonal 
B)  not orthogonal 
A)  orthogonal 
B)  not orthogonal

Question 2

Compute the cross product a × b.

Accepted Answer

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

Question 3

Use the parallelpiped volume formula to determine if the vectors are coplanar.

Accepted Answer

A)  coplanar 
B)  not coplanar 
A)  coplanar 
B)  not coplanar

Question 4

Find parametric equations of the line through   and perpendicular to both   and   .

Accepted Answer

The answer of Find parametric equations of the line through...

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

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 7

Find two unit vectors parallel to the given vector.

Accepted Answer

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

Question 8

Compute 2a - 3b.

Accepted Answer

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

Question 9

Determine whether the given lines are the same. x = 9 - t, y = -2 - 3t, z = 5 - 8t and x = 10 - 2t, y = 1 - 6t, z = 13 - 16t

Accepted Answer

A)  The lines are the same. 
B)  The lines are not the same. 
A)  The lines are the same. 
B)  The lines are not the same.

Question 10

Who is doing more work: a weight lifter who is holding a 450-pound barbell motionless over his head, or senior citizen sitting on a park bench? Explain.

Accepted Answer

The two individuals are doing

Question 11

Assume that the ball is moving into the page (and away from you) with the indicated spin. Determine the direction of the Magnus force.

Accepted Answer

A)  to the right 
B)  to the left 
C)  up 
D)  down 
E)  The Magnus force is zero. 
A)  to the right 
B)  to the left 
C)  up 
D)  down 
E)  The Magnus force is zero.

Question 12

Find projb a for the given vectors.

Accepted Answer

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

Question 13

Suppose two airplanes fly paths described by the parametric equations   where s and t represent time. Determine whether the flight paths intersect and, if so, whether the planes collide.

Accepted Answer

A)  The paths do not intersect. 
B)  The paths intersect, but the planes do not collide. 
C)  The paths intersect and the planes collide. 
A)  The paths do not intersect. 
B)  The paths intersect, but the planes do not collide. 
C)  The paths intersect and the planes collide.

Question 14

Find symmetric equations of the line through   and parallel to   .

Accepted Answer

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

Question 15

Find parametric equations of the line through   parallel to   .

Accepted Answer

The answer of Find parametric equations of the line through...

Question 16

Illustrate the sum a + b graphically. a = -2i - j; b = -3i + 2j

Accepted Answer

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

Question 17

Use the parallelpiped volume formula to determine if the vectors are coplanar.

Accepted Answer

A)  coplanar 
B)  not coplanar 
A)  coplanar 
B)  not coplanar

Question 18

Find an equation of the given plane. The plane containing the point   with normal vector

Accepted Answer

A)  3x + y + 7z = -22 
B)  2x + 7y - 5z = 0 
C)  2x + 7y - 5z = -22 
D)  2x + 7y - 5z = 11 
A)  3x + y + 7z = -22 
B)  2x + 7y - 5z = 0 
C)  2x + 7y - 5z = -22 
D)  2x + 7y - 5z = 11

Question 19

Sketch the given plane. y + 2z = 6

Accepted Answer

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

Question 20

Find the vector with the given polar form.

Accepted Answer

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

Determine if the vectors are orthogonal.

Compute the cross product a × b.

Use the parallelpiped volume formula to determine if the vectors are coplanar.

Find parametric equations of the line through and perpendicular to both and .

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

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

Find two unit vectors parallel to the given vector.

Compute 2a - 3b.

Determine whether the given lines are the same. x = 9 - t, y = -2 - 3t, z = 5 - 8t and x = 10 - 2t, y = 1 - 6t, z = 13 - 16t

Who is doing more work: a weight lifter who is holding a 450-pound barbell motionless over his head, or senior citizen sitting on a park bench? Explain.

Assume that the ball is moving into the page (and away from you) with the indicated spin. Determine the direction of the Magnus force.

Find proj_ba for the given vectors.

Suppose two airplanes fly paths described by the parametric equations where s and t represent time. Determine whether the flight paths intersect and, if so, whether the planes collide.

Find symmetric equations of the line through and parallel to .

Find parametric equations of the line through parallel to .

Illustrate the sum a + b graphically. a = -2i - j; b = -3i + 2j

Use the parallelpiped volume formula to determine if the vectors are coplanar.

Find an equation of the given plane. The plane containing the point with normal vector

Sketch the given plane. y + 2z = 6

Find the vector with the given polar form.

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

Determine if the vectors are orthogonal.

Compute the cross product a × b.

Use the parallelpiped volume formula to determine if the vectors are coplanar.

Find parametric equations of the line through and perpendicular to both and .

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

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

Find two unit vectors parallel to the given vector.

Compute 2a - 3b.

Determine whether the given lines are the same. x = 9 - t, y = -2 - 3t, z = 5 - 8t and x = 10 - 2t, y = 1 - 6t, z = 13 - 16t

Who is doing more work: a weight lifter who is holding a 450-pound barbell motionless over his head, or senior citizen sitting on a park bench? Explain.

Assume that the ball is moving into the page (and away from you) with the indicated spin. Determine the direction of the Magnus force.

Find projb a for the given vectors.

Suppose two airplanes fly paths described by the parametric equations where s and t represent time. Determine whether the flight paths intersect and, if so, whether the planes collide.

Find symmetric equations of the line through and parallel to .

Find parametric equations of the line through parallel to .

Illustrate the sum a + b graphically. a = -2i - j; b = -3i + 2j

Use the parallelpiped volume formula to determine if the vectors are coplanar.

Find an equation of the given plane. The plane containing the point with normal vector

Sketch the given plane. y + 2z = 6

Find the vector with the given polar form.

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

Find proj_ba for the given vectors.