Question 1

Compute ||2a - 3b||.

Accepted Answer

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

Question 2

Find the indicated area. Area of the parallelogram with two adjacent sides formed by   and

Accepted Answer

A)    
B)  7 
C)  43 
D)    
A)    
B)  7 
C)  43 
D)

Question 3

Compute the cross product a × b.

Accepted Answer

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

Question 4

Find the vector with initial point A and terminal point B. A = (4, 2), B = (-3, -7)

Accepted Answer

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

Question 5

Illustrate the difference a - b graphically. a = -i + 4j; b = -3i + 3j

Accepted Answer

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

Question 6

Show that   . Show all of your work.

Accepted Answer

The answer of Show that   . Show all...

Question 7

Compute -a - 2b.

Accepted Answer

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

Question 8

Find the distance from the point Q to the given line. Round to the nearest thousandth.   , line through   and

Accepted Answer

A)  14.036 
B)  0.644 
C)  11.460 
D)  12.992 
A)  14.036 
B)  0.644 
C)  11.460 
D)  12.992

Question 9

Which of the following statements are true? i.   ii.   iii.

Accepted Answer

A)  i only 
B)  ii only 
C)  i and ii only 
D)  i and iii only 
E)  iii only 
A)  i only 
B)  ii only 
C)  i and ii only 
D)  i and iii only 
E)  iii only

Question 10

Find a unit vector in the same direction as the given vector. -2i + 5j

Accepted Answer

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

Question 11

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 12

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 13

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 14

Find a vector with the given magnitude and in the same direction as the given vector. Magnitude 7,

Accepted Answer

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

Question 15

Find the distance between the given points. (0, -3, -1), (3, 6, 8)

Accepted Answer

A)    
B)  171 
C)    
D)  67 
A)    
B)  171 
C)    
D)  67

Question 16

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 17

Identify the surface.

Accepted Answer

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

Question 18

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

Accepted Answer

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

Question 19

Find an equation of the sphere with radius 2 and center (-2, 6, 8).

Accepted Answer

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

Question 20

Sketch the given plane. 3x - y + 2z = 6

Accepted Answer

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

Compute ||2a - 3b||.

Find the indicated area. Area of the parallelogram with two adjacent sides formed by and

Compute the cross product a × b.

Find the vector with initial point A and terminal point B. A = (4, 2), B = (-3, -7)

Illustrate the difference a - b graphically. a = -i + 4j; b = -3i + 3j

Show that . Show all of your work.

Compute -a - 2b.

Find the distance from the point Q to the given line. Round to the nearest thousandth. , line through and

Which of the following statements are true? i. ii. iii.

Find a unit vector in the same direction as the given vector. -2i + 5j

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.

Identify the surface.

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

Find a vector with the given magnitude and in the same direction as the given vector. Magnitude 7,

Find the distance between the given points. (0, -3, -1), (3, 6, 8)

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

Identify the surface.

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

Find an equation of the sphere with radius 2 and center (-2, 6, 8).

Sketch the given plane. 3x - y + 2z = 6

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

Compute ||2a - 3b||.

Find the indicated area. Area of the parallelogram with two adjacent sides formed by and

Compute the cross product a × b.

Find the vector with initial point A and terminal point B. A = (4, 2), B = (-3, -7)

Illustrate the difference a - b graphically. a = -i + 4j; b = -3i + 3j

Show that . Show all of your work.

Compute -a - 2b.

Find the distance from the point Q to the given line. Round to the nearest thousandth. , line through and

Which of the following statements are true? i. ii. iii.

Find a unit vector in the same direction as the given vector. -2i + 5j

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.

Identify the surface.

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

Find a vector with the given magnitude and in the same direction as the given vector. Magnitude 7,

Find the distance between the given points. (0, -3, -1), (3, 6, 8)

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

Identify the surface.

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

Find an equation of the sphere with radius 2 and center (-2, 6, 8).

Sketch the given plane. 3x - y + 2z = 6

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