4.2.1 What Does a Vector Look Like? ......................37
4.2.2 Position vs. Displacement .........................38
4.2.3 Specifying Vectors .............................38
4.2.4 Vectors as a Sequence of Displacements .................39
4.3 Vectors vs. Points ................................40
4.3.1 Relative Position ..............................41
4.3.2 The Relationship Between Points and Vectors ..............41
4.4 Exercises.....................................42
Chapter 5 Operations on Vectors .................45
5.1 Linear Algebra vs. What We Need .......................46
5.2 Typeface Conventions..............................46
5.3 The Zero Vector .................................47
5.4 Negating a Vector ................................48
5.4.1 Official Linear Algebra Rules .......................48
5.4.2 Geometric Interpretation ..........................48
5.5 Vector Magnitude (Length) ...........................49
5.5.1 Official Linear Algebra Rules .......................49
5.5.2 Geometric Interpretation ..........................50
5.6 Vector Multiplication by a Scalar ........................51
5.6.1 Official Linear Algebra Rules .......................51
5.6.2 Geometric Interpretation ..........................52
5.7 Normalized Vectors ...............................53
5.7.1 Official Linear Algebra Rules .......................53
5.7.2 Geometric Interpretation ..........................53
5.8 Vector Addition and Subtraction ........................54
5.8.1 Official Linear Algebra Rules .......................54
5.8.2 Geometric Interpretation ..........................55
5.8.3 Vector from One Point to Another .....................57
5.9 The Distance Formula..............................57
5.10 Vector Dot Product...............................58
5.10.1 Official Linear Algebra Rules ......................58
5.10.2 Geometric Interpretation .........................59
5.10.3 Projecting One Vector onto Another ...................61
5.11 Vector Cross Product..............................62
5.11.1 Official Linear Algebra Rules ......................62
5.11.2 Geometric Interpretation .........................62
5.12 Linear Algebra Identities ...........................65
5.13 Exercises ....................................67
Chapter 6 A Simple 3D Vector Class ................69
6.1 Class Interface ..................................69
6.2 Class Vector3 Definition ............................70
6.3 Design Decisions ................................73
6.3.1 Floats vs. Doubles .............................73
6.3.2 Operator Overloading ...........................73
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Contents
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