Question 1

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)    A

Question 2

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

Accepted Answer

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

Question 3

Compute   .

Accepted Answer

A)    
B)  -1 
C)    
D)  6529 
A)    
B)  -1 
C)    
D)  6529 B

Question 4

Use geometry to identify the cross product.

Accepted Answer

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

Question 5

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

Accepted Answer

A)  -5x - 3y + 9z = -30 
B)  9x - 8y - z = 0 
C)  9x - 8y - z = -30 
D)  9x - 8y - z = 1 
A)  -5x - 3y + 9z = -30 
B)  9x - 8y - z = 0 
C)  9x - 8y - z = -30 
D)  9x - 8y - z = 1

Question 6

A constant force of   pounds moves an object in a straight line from the point (0, 0) to the point (23, -15). Compute the work done.

Accepted Answer

A)  -595 
B)  0 
C)  -635 
D)  865 
A)  -595 
B)  0 
C)  -635 
D)  865

Question 7

Find projb a for the given vectors.

Accepted Answer

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

Question 8

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 9

Determine if the vectors are orthogonal.

Accepted Answer

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

Question 10

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

Accepted Answer

A)  1.571 
B)  0.056 
C)  0.239 
D)  1.332 
A)  1.571 
B)  0.056 
C)  0.239 
D)  1.332

Question 11

Identify the surface.

Accepted Answer

A)  hyperboloid of two sheets 
B)  cone 
C)  hyperboloid of one sheet 
D)  hyperbolic paraboloid 
A)  hyperboloid of two sheets 
B)  cone 
C)  hyperboloid of one sheet 
D)  hyperbolic paraboloid

Question 12

Compute 3a + 5b.

Accepted Answer

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

Question 13

Compute a + b.

Accepted Answer

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

Question 14

Write the given vector as the product of its magnitude and a unit vector. (Write the unit vector so that it is in the same direction as the given vector. This means that the signs of the components of the unit vector should be the same as the signs of the corresponding components of the given vector.)

Accepted Answer

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

Question 15

Write the given vector as the product of its magnitude and a unit vector. (Write the unit vector so that it is in the same direction as the given vector. This means that the signs of the components of the unit vector should be the same as the signs of the corresponding components of the given vector.) From   to

Accepted Answer

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

Question 16

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 17

Identify the surface.

Accepted Answer

A)  elliptic paraboloid 
B)  cone 
C)  hyperboloid of one sheet 
D)  hyperbolic paraboloid 
A)  elliptic paraboloid 
B)  cone 
C)  hyperboloid of one sheet 
D)  hyperbolic paraboloid

Question 18

If you apply a force of magnitude 33 pounds at the end of an 10-inch wrench at an angle of   to the wrench, find the magnitude of the torque applied to the bolt. Round to the nearest tenth of an inch-pound.

Accepted Answer

A)  23.8 in-lb 
B)  165.0 in-lb 
C)  13.8 in-lb 
D)  285.8 in-lb 
A)  23.8 in-lb 
B)  165.0 in-lb 
C)  13.8 in-lb 
D)  285.8 in-lb

Question 19

Find the angle between the lines. Round to the nearest hundredth of a radian.

Accepted Answer

A)  1.71 
B)  0.14 
C)  3.01 
D)  0.78 
A)  1.71 
B)  0.14 
C)  3.01 
D)  0.78

Question 20

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

Accepted Answer

Answer may vary. Fin

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

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

Compute .

Use geometry to identify the cross product.

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

A constant force of pounds moves an object in a straight line from the point (0, 0) to the point (23, -15). Compute the work done.

Find proj_ba for the given vectors.

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

Determine if the vectors are orthogonal.

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

Identify the surface.

Compute 3a + 5b.

Compute a + b.

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

Identify the surface.

If you apply a force of magnitude 33 pounds at the end of an 10-inch wrench at an angle of to the wrench, find the magnitude of the torque applied to the bolt. Round to the nearest tenth of an inch-pound.

Find the angle between the lines. Round to the nearest hundredth of a radian.

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

Preliminaries

Limits and Continuity

Differentiation

Applications of the Derivative

Integration

Applications of the Definite Integral

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 11: Vectors and the Geometry of Space

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

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

Compute .

Use geometry to identify the cross product.

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

A constant force of pounds moves an object in a straight line from the point (0, 0) to the point (23, -15). Compute the work done.

Find projb a for the given vectors.

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

Determine if the vectors are orthogonal.

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

Identify the surface.

Compute 3a + 5b.

Compute a + b.

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

Identify the surface.

If you apply a force of magnitude 33 pounds at the end of an 10-inch wrench at an angle of to the wrench, find the magnitude of the torque applied to the bolt. Round to the nearest tenth of an inch-pound.

Find the angle between the lines. Round to the nearest hundredth of a radian.

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

Preliminaries

Limits and Continuity

Differentiation

Applications of the Derivative

Integration

Applications of the Definite Integral

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.