Question 1

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

Accepted Answer

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

Question 2

Determine if the lines are parallel, skew or intersect.

Accepted Answer

A)  parallel 
B)  skew 
C)  intersect 
A)  parallel 
B)  skew 
C)  intersect

Question 3

Find the distance between the given objects. The point   and the plane -7x - 6y + 5z = 7

Accepted Answer

A)    
B)    
C)  0 
D)    
A)    
B)    
C)  0 
D)

Question 4

Find a vector with the given magnitude in the same direction as the given vector. magnitude 2, v = 5i - j

Accepted Answer

A)  10i - 2j 
B)    
C)    
D)  2i 
A)  10i - 2j 
B)    
C)    
D)  2i

Question 5

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

Accepted Answer

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

Question 6

Find an equation of the given plane. The plane containing the points   ,   and

Accepted Answer

A)  4x - 9y - 3z = 63 
B)  3x - 18y - z = 106 
C)  3x - 18y - z = 0 
D)  86x + 17y - 48z = 335 
A)  4x - 9y - 3z = 63 
B)  3x - 18y - z = 106 
C)  3x - 18y - z = 0 
D)  86x + 17y - 48z = 335

Question 7

Use geometry to identify the cross product.

Accepted Answer

A)  -5j 
B)  0 
C)  5i 
D)  5k 
A)  -5j 
B)  0 
C)  5i 
D)  5k

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

Determine if the lines are parallel, skew or intersect.

Find the distance between the given objects. The point and the plane -7x - 6y + 5z = 7

Find a vector with the given magnitude in the same direction as the given vector. magnitude 2, v = 5i - j

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

Find an equation of the given plane. The plane containing the points , and

Use geometry to identify the cross product.

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

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

Determine if the lines are parallel, skew or intersect.

Find the distance between the given objects. The point and the plane -7x - 6y + 5z = 7

Find a vector with the given magnitude in the same direction as the given vector. magnitude 2, v = 5i - j

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

Find an equation of the given plane. The plane containing the points , and

Use geometry to identify the cross product.

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