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APPENDIX A Vectors CONTENTS A.1 Scaling a vector . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321 A.2 Unit or Direction vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321 A.3 Vector addition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322 A.4 Vector subtraction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322 A.5 Points and vectors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322 A.6 Parametric definition of lines and rays . . . . . . . . . . . . . . . . . . . . . . . . 323 A.7 Dot or inner product . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323 A.8 A.7.1 Trigonometric interpretation of dot product . . . . . . . . . 324 A.7.2 Geometric interpretation of dot product . . . . . . . . . . . . . 324 A.7.3 Dot product example: The distance from a point to a line . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325 A.7.4 Dot product example: Mirror reflection . . . . . . . . . . . . . . 325 Cross Product . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326 A.8.1 Trigonometric interpretation of cross product . . . . . . . 326 A.8.2 Cross product example: Finding surface normals . . ...
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