P

X

$\vec{a}$

$\vec{b}$

$\vec{b_{\parallel}}$

$\vec{b_{\perp}}$

$\vec{a}_{\parallel}$

$\vec{a}_{\perp}$

Projektion auf Vektor b

O: (0, 0)
A = (3.316583798466424, 1.0195459520670358)
a = Vector(O, A)
B = (1.2748624561029023, 2.771769492155128)
b = Vector(O, B)
c: (a * b)
d: (abs(a) * abs(b))
Text2: "|\vec{a}| \cdot |\vec{b}| = \sqrt{" + (LaTeX[(x(a))^(2)]) + "+" + (LaTeX[(y(a))^(2)]) + "} \cdot \sqrt{" + (LaTeX[(x(b))^(2)]) + "+" + (LaTeX[(y(b))^(2)]) + "} = " + (LaTeX[d]) + ""
f = Line(O, A)
g_{1} = OrthogonalLine(B, f)
C = Intersect(f, g_{1})
u = Vector(O, C)
v = Vector(C, B)
e: (a * u)
Text3: "\vec{a} \cdot \vec{b_{\parallel}} =  \left( \begin{array}{c} " + (LaTeX[x(a)]) + " \\ " + (LaTeX[y(a)]) + " \end{array} \right) \cdot\left( \begin{array}{c} " + (LaTeX[x(u)]) + " \\ " + (LaTeX[y(u)]) + " \end{array} \right) = (" + (LaTeX[x(a)]) + ") \cdot (" + (LaTeX[x(u)]) + ")+ (" + (LaTeX[y(a)]) + ") \cdot (" + (LaTeX[y(u)]) + ") = " + (LaTeX[e]) + ""
α = Angle(a, b)
i: cos(α)
j: abs(a)
k: abs(u)
l: (abs(a) * abs(u))
Text4: "cos(\alpha)= " + (LaTeX[i]) + ""
m: abs(b)
Text5: "\underbrace{|\vec{a}|}_{" + (LaTeX[j]) + "} \cdot \underbrace{|\vec{b_{\parallel}}|}_{" + (LaTeX[k]) + "} = " + (LaTeX[l]) + ""
s: ((abs(a) * abs(b)) * i)
Text1: "\vec{a} \cdot \vec{b} =  \underbrace{\left( \begin{array}{c} " + (LaTeX[x(a)]) + " \\ " + (LaTeX[y(a)]) + " \end{array} \right)}_{\text{Vektor}} \cdot \underbrace{\left( \begin{array}{c} " + (LaTeX[x(b)]) + " \\ " + (LaTeX[y(b)]) + " \end{array} \right)}_{\text{Vektor}} = (" + (LaTeX[x(a)]) + ") \cdot (" + (LaTeX[x(b)]) + ")+ (" + (LaTeX[y(a)]) + ") \cdot (" + (LaTeX[y(b)]) + ") =\underbrace{ " + (LaTeX[c]) + "}_{\text{Zahl}}"
h = OrthogonalLine(A, b)
n = Line(O, B)
D = Intersect(h, n)
w = Vector(O, D)
p = Vector(D, A)
q = true
g = OrthogonalLine(O, b)
t = OrthogonalLine(A, g)
E = Intersect(g, t)
f_1 = Segment(A, E)
a_1: abs(w)
Text7: "\vec{a} \cdot \vec{b} =\vec{a}_{\parallel} \cdot \vec{b} = |\vec{a}_{\parallel}|  \cdot |\vec{b}|  = " + (LaTeX[a_1]) + " \cdot " + (LaTeX[m]) + " = " + (LaTeX[s]) + ""