向量 Vector

(1) 有方向的線段(Represented by a directed line segment)

A ≠ B

C ＝ A (如果∣C∣∣A∣長度及方向一樣)

(2) 向量的相加(Addition of Vector)

C= A + B

註：在一般情況下 ∣C∣≠∣A∣＋∣B∣

如 A＋B＝0, → A＝－B

(3) 向量的分量(Components of a vector)

A = A_xi + A_yj

i, j = 在x, y的方向的單位向量(unit vectors)

A_x = A cosq, A_y = A sinq

∣A∣ =

= A --------- A 的大小

q = tan

在三維空間 (3-dimension)

A = A_xi + A_yj + A_zk

∣A∣ =

單位向量 (Unit vector)：A =

∣A∣= 1 　

(4) 向量的乘法(Multiplication of Vectors)

(a) 純量積 ( 點積 ) Scalar product (dot product)

( 純量 ) A．B＝AB cosθ = A_xB_x + A_yB_y + A_zB_z (i．i = 1 = j．j = k．k, i．j = 0 = j．k 等
θ= 90°or cosθ = 0) (b) 向量積 (叉積) Vector product (cross product)

(新的向量) A×B = AB sinθn

      n = 垂直於 A 及 B 兩者的單位向量

註：

i×i = 0   θ= 0   或   sinθ= 0

j×j = 0 = k×k
或 A×A = 0 (為所有A)
i×j = k, j×k = i, k×i = j
A×B    = (A_yB_z - A_zB_y)i + (A_zB_x - A_xB_z)j + (A_xB_y - A_yB_x)k
   =