Table of contents
Preface
This module contains review questions and answers keyed to the module titled GAME 2302-0130: Putting the Game-Math Library to Work .
The questions and the answers are connected by hyperlinks to make it easy for you to navigate from the question to the answer and back again.
Questions
Question 1 .
What is the length of the vector represented by (3,0)T where the upper-case T indicates "transpose" and is often shown as an upper-case superscript T.
- A. 2
- B. 3
- C. 4
- D. 5
Question 2
True or False: When a 2D vector is aligned with the x axis, the column matrix that represents it has a non-zero value in the first element, and zero for the second element.
Question 3
True or False: When a 2D vector is aligned with the y axis, the column matrix that represents it has a non-zero value in the first element, and zero for thesecond element.
Question 4
What is the length of the vector represented by (0,4)T
- A. 2
- B. 3
- C. 4
- D. 5
Question 5
What is the length of the hypotenuse of a right triangle whose two sides are 6 and 8?
- A. 6
- B. 8
- C. 10
- D. 12
Question 6
What is the length of the vector represented by ( 4, 3 )T
- A. 3
- B. 4
- C. 5
- D. 6
Question 7
Given: The length of the vector v is often represented as |v|
Question: What is the value of |( 4, 3 )T|
- A. 3
- B. 4
- C. 5
- D. 6
Question 8
True or False: Given vectors u and v, the following is a true statement where>= indicates "greater than or equal"
|u + v|>= |u| + |v|
Question 9
True or False: Three dimensional vectors have length.
Question 10
Given:
- The ^ character represents exponentiation
- sqrt() represents computation of the square root of the value contained in the parentheses.
- (x,y,z)T is a transpose column matrix that represents a three-dimensional vector
True or False: The following statement is true.
|(x,y,z)T| = sqrt(x^3 + y^3 + z^3)
Question 11
What is the value of |(2,-4,4)T|
- A. 4
- B. 5
- C. 6
- D. 7
Question 12
True or False: Length is a property of a vector and is not a property of the column matrix that is used to represent it.
Question 13
True or False: The length of a vector can be positive or negative.
Question 14
True or False: Two vectors that are equal to each other must have the same length.
Question 15
True or False: Two vectors that have the same length must be equal to each other.
Question 16
True or False: If v is a vector, then -v is a vector that is perpendicular to v.
Question 17
Given: the vector represented by (4,0)T
True or False: The vector is parallel to the X axis of the coordinate frame we are using. Often this is horizontal, pointing right. (Or, you might say that the vector is oriented at 0 degrees if you consider due East to be 0degrees.)
Question 18
Given: The orientation of a vector is usually expressed as an angle with the positive x axis of a coordinate frame. There are two ways of doing this: