Chapter 3 Vectors第 3 章 向量

Chapter 3 Vector Quantities3-1 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

3-1 What is Physics?

• Size

• Direction

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

Displacement vector

3-3 Adding Vectors Geometrically

• Vector sum 向量和 (resultant 合量 )

s a b

s a b

a b b a

( ) ( )a b c a b c

( ) 0b b

( )d a b a b

commutative law交換律

associative law結合律

commutative law

a b b a

associative law

( ) ( )a b c a b c

( ) 0b b

( )d a b a b

Sample Problem

3-4 Components of Vectors

• A component ( 分量 ) of a vector is the projection of the vector on an axis

2 2

cos and sin

and tan

x y

yx y

x

a a a a

aa a a

a

Resolving the vector 向量分解

Vector Notation 向量記號• component notation

• magnitude-angle notation

2 2

cos and sin

and tan

x y

yx y

x

a a a a

aa a a

a

Sample Problem

Trigonometric function

• hypotenuse 斜邊• degree 度• radian 弧度、弳、弳度 (rad)

鄰邊

對邊

Inverse trigonometric functions反三角函數

= sin1

= cos1

= tan1

3-5 Unit Vectors 單位向量

• right-handed coordinate system 右手坐標系

ˆ ˆ ˆ ˆi j i jx y x ya a a b b b

3-6 Adding Vectors by Components

x x x

y y y

z z z

r a b

r a b

r a b

r a b

Sample Problem

Sample Problem

3-7 Vectors and the Laws of Physics

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 ),

Scalar Product

Vector Product

Vector Product

Vector Product