平面向量的正射影
Author: 藍邦偉  老師

Proj_vu

平面向量的正射影

 \overrightarrow{u} = (

a_1

,

b_1

)

 \overrightarrow{v} =(

a_2

,

b_2

)

Proj_\overrightarrow{v}\overrightarrow{u}

b_2 = -4 (slider from -10 to 10, step 1)
O = Intersect(xAxis, yAxis)
a_2 = -4 (slider from -10 to 10, step 1)
B: (a_2, b_2)
c = Line(O, B)
v = Vector(O, B)
b_1 = 7 (slider from -10 to 10, step 1)
a_1 = -3 (slider from -10 to 10, step 1)
A: (a_1, b_1)
a = OrthogonalLine(A, v)
u = Vector(O, A)
b = Segment(O, B)
H = Intersect(a, c)
d = Segment(A, H)
w = Vector(O, H)
T_1: (x(Corner[1]), 0)
T_2: (x(Corner[2]), 0)
T_3: (0, y(Corner[1]))
z = Vector(T_1, T_2)
T_4: (0, y(Corner[4]))
e = Vector(T_3, T_4)
inputBox1 = Textfield(a_1)
inputBox2 = Textfield(b_1)
文字1: " \vec{ u } =(" + (LaTeX[a_1]) + "," + (LaTeX[b_1]) + ")在 \vec{ v } =(" + (LaTeX[a_2]) + "," + (LaTeX[b_2]) + ")上的正射影"
文字4: "=(" + (LaTeX[(a_1 * a_2 + b_1 * b_2) * a_2 / (a_2^(2) + b_2^(2))]) + "," + (LaTeX[(a_1 * a_2 + b_1 * b_2) * b_2 / (a_2^(2) + b_2^(2))]) + ")"
inputBox3 = Textfield(a_2)
inputBox4 = Textfield(b_2)
文字3: "=\frac{(" + (LaTeX[a_1]) + ")\cdot(" + (LaTeX[a_2]) + ")+(" + (LaTeX[b_1]) + ")\cdot(" + (LaTeX[b_2]) + ")}{" + (LaTeX[a_2^(2)]) + "+" + (LaTeX[b_2^(2)]) + "}(" + (LaTeX[a_2]) + "," + (LaTeX[b_2]) + ")"