平面向量的內積
Author: 藍邦偉  老師

 \vec{ a } 

 \vec{ b } 

 \vec{ a } - \vec{ b } 

| \vec{ a } - \vec{ b }|²=| \vec{ a }  |²+| \vec{ b }|²-2| \vec{ a }|| \vec{ b }|cosθ   

⇒| \vec{ a }|² -2 \vec{ a } \vec{ b }+| \vec{ b }|²=| \vec{ a }  |²+| \vec{ b }|²-2| \vec{ a }|| \vec{ b }|cosθ 

⇒ \vec{ a }\cdot{}  \vec{ b } =| \vec{ a } || \vec{ b }|cosθ 

向量的內積

u = Vector((x(Corner[1]), 0), (x(Corner[3]), 0))
v = Vector((0, y(Corner[1])), (0, y(Corner[3])))
O = (2.7271074380165308, 4.790185950413228)
A = (4.504958677685953, 2.0925619834710742)
a = Vector(O, A)
B = (7.5370247933884364, 4.476136363636369)
b = Vector(O, B)
α = Angle(B, O, A)
c = Vector(B, A)
a_1 = Segment(O, A)
b_1 = Segment(O, B)
n = 0 (slider from 0 to 5, step 1)
文字8: "=" + (LaTeX[a_1]) + "\times{}" + (LaTeX[b_1]) + "\times{}cos" + (LaTeX[α]) + ""
文字9: "=" + (LaTeX[a_1 * b_1 * cos(α)]) + ""