平面向量的正射影
Author: 藍邦偉  老師

Proj_u v

平面向量的正射影

b_2 = -6 (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)
文字1: " \vec{ u } =(" + a_1 + "," + b_1 + ")在 \vec{ v } =(" + a_2 + "," + b_2 + ")上的正射影"
文字4: "=(" + ((a_1 * a_2 + b_1 * b_2) * a_2 / (a_2^(2.0) + b_2^(2.0))) + "," + ((a_1 * a_2 + b_1 * b_2) * b_2 / (a_2^(2.0) + b_2^(2.0))) + ")"
T_1: (x(Corner[1.0]), 0.0)
T_2: (x(Corner[2.0]), 0.0)
T_3: (0.0, y(Corner[1.0]))
z = Vector(T_1, T_2)
T_4: (0.0, y(Corner[4.0]))
e = Vector(T_3, T_4)
文字3: "Proj_ \vec{ u } \vec{ v }=" + "\frac{(" + a_1 + ")\times(" + a_2 + ")+(" + b_1 + ")\times(" + b_2 + ")}{" + (a_2^(2.0)) + "+" + (b_2^(2.0)) + "}" + "(" + a_2 + "," + b_2 + ")"