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Mastering Vector Theory in Physics

Dive into vectors and scalars, vector components, unit vectors, and vector multiplication with geometric and algebraic approaches in physics.

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Mastering Vector Theory in Physics

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  1. Chapter 3 Vectors第3章 向量

  2. Chapter 3 Vector Quantities 3-1 What is Physics? 3-2 Vectors and Scalars 3-3 Adding Vectors Geometrically 3-4 Components of Vectors 3-5 Unit Vectors 3-6 Adding Vectors by Components 3-7 Vectors and the Laws of Physics 3-8 Multiplying Vectors

  3. 3-1 What is Physics? • Size • Direction

  4. 3-2 Vectors and Scalars向量與純量 • Vector • magnitude 量值 • direction 方向 • Vector quantities • Displacement, velocity, and acceleration • Scalar quantities • Temperature, pressure, energy, mass, and time

  5. Displacement vector

  6. 3-3 Adding Vectors Geometrically • Vector sum 向量和 (resultant 合量)

  7. commutative law 交換律 associative law 結合律

  8. commutative law

  9. associative law

  10. Sample Problem

  11. 3-4 Components of Vectors • A component (分量) of a vector is the projection of the vector on an axis

  12. Resolving the vector 向量分解

  13. Vector Notation 向量記號 • component notation • magnitude-angle notation

  14. Sample Problem

  15. Trigonometric function 對邊 鄰邊 • hypotenuse 斜邊 • degree 度 • radian 弧度、弳、弳度 (rad)

  16. Inverse trigonometric functions反三角函數 •  = sin1 •  = cos1 •  = tan1

  17. 3-5 Unit Vectors 單位向量 • right-handed coordinate system 右手坐標系

  18. 3-6 Adding Vectors by Components

  19. Sample Problem

  20. Sample Problem

  21. 3-7 Vectors and the Laws of Physics

  22. 3-8 Multiplying Vectors • Multiplying a Vector by a Scalar • Multiplying a Vector by a Vector • scalar product (純量積), dot product (點積), inner product (內積) • vector product (向量積), cross product (叉積), outer product (外積),

  23. Scalar Product

  24. Vector Product

  25. Vector Product

  26. Vector Product

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