向量內積的座標表示法
Author: 藍邦偉  老師

A(x_1,y_1)

B(x_2,y_2)

 \vec{ a } 

 \vec{ b } 

  \overline{ AB }²= \overline{ OA }²+ \overline{ OB }²-2 \overline{ OA } \cdot{}\overline{ OB }cosθ      

⇒(x_2-x_1)²+(y_2-y_1)²

⇒-2(x_1x_2+y_1y_2)=-2 \vec{ a }\cdot{}  \vec{ b } 

向量內積的座標表示法

⇒\vec{ a } \cdot{} \vec{ b } =x_1x_2+y_1y_2

=(x_1²+y_1²)+(x_2²+y_2²)-2 \vec{ a } \cdot{}\vec{ b }  

u = Vector((x(Corner[1]), 0), (x(Corner[3]), 0))
v = Vector((0, y(Corner[1])), (0, y(Corner[3])))
O = (0, 0)
A = (4, 2)
a = Vector(O, A)
B = (1, 4)
b = Vector(O, B)
θ = Angle(B, O, A)
a_1 = Segment(O, A)
b_1 = Segment(O, B)
n = 0 (slider from 0 to 6, step 1)
c = Segment(B, A)
T_1 = Corner(1)
T_4 = Corner(4)
T_2: 0.6 * Corner[1] + 0.4 * Corner[2]
T_3: 0.6 * Corner[4] + 0.4 * Corner[3]
多邊形1, t_1, t_2, t_3, t_4 = Polygon(T_1, T_2, T_3, T_4)
d = Segment(T_2, T_3)
文字9: "=(" + (LaTeX[x(A)]) + ")(" + (LaTeX[x(B)]) + ")+(" + (LaTeX[y(A)]) + ")(" + (LaTeX[y(B)]) + ")"
文字10: "=" + (LaTeX[x(A) * x(B) + y(A) * y(B)]) + ""