1.12 Game0130r: review

Table of contents

• Preface
• Questions
  • 1 , 2 , 3 , 4 , 5 , 6 , 7 , 8 , 9 , 10 , 11 , 12 , 13 , 14 , 15 , 16 , 17 , 18 , 19 , 20 , 21 , 22 , 23
• Answers
• Miscellaneous

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

Answer 1

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.

Answer 2

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.

Answer 3

Question 4

What is the length of the vector represented by (0,4)T

• A. 2
• B. 3
• C. 4
• D. 5

Answer 4

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

Answer 5

Question 6

What is the length of the vector represented by ( 4, 3 )T

• A. 3
• B. 4
• C. 5
• D. 6

Answer 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

Answer 7

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|

Answer 8

Question 9

True or False: Three dimensional vectors have length.

Answer 9

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)

Answer 10

Question 11

What is the value of |(2,-4,4)T|

• A. 4
• B. 5
• C. 6
• D. 7

Answer 11

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.

Answer 12

Question 13

True or False: The length of a vector can be positive or negative.

Answer 13

Question 14

True or False: Two vectors that are equal to each other must have the same length.

Answer 14

Question 15

True or False: Two vectors that have the same length must be equal to each other.

Answer 15

Question 16

True or False: If v is a vector, then -v is a vector that is perpendicular to v.

Answer 16

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.)

Answer 17

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: