Question 1

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 2

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 3

Find an equation of the sphere with radius 11 and center (2, -4, 4).

Accepted Answer

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

Question 4

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 5

Determine whether the given planes are the same. 5(x + 2) + (y - 9) + 7(z + 7) = 0
5(x + 3) + (y - 6) + 7(z - 6) = 0

Accepted Answer

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

Question 6

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

Accepted Answer

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

Question 7

Compute the given determinant.

Accepted Answer

A)  -24 
B)  4 
C)  24 
D)  -4 
A)  -24 
B)  4 
C)  24 
D)  -4

Identify the surface.

Identify the surface.

Find an equation of the sphere with radius 11 and center (2, -4, 4).

Determine whether the given planes are the same. 5(x + 2) + (y - 9) + 7(z + 7) = 0 5(x + 3) + (y - 6) + 7(z - 6) = 0

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

Compute the given determinant.

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

Identify the surface.

Identify the surface.

Find an equation of the sphere with radius 11 and center (2, -4, 4).

Determine whether the given planes are the same. 5(x + 2) + (y - 9) + 7(z + 7) = 0 5(x + 3) + (y - 6) + 7(z - 6) = 0

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

Compute the given determinant.

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