$\vec{a}$

$\vec{b}$

$\vec{b_{\parallel}}$

$\vec{b_{\perp}}$

O: (0, 0)
A = (6, 2)
B = (3, 3)
a = Vector(O, A)
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 = OrthogonalLine(B, f)
C = Intersect(f, g)
u = Vector(O, C)
v = Vector(C, B)
Text1: "\vec{a} \cdot \vec{b} =  \left( \begin{array}{c} " + (LaTeX[x(a)]) + " \\ " + (LaTeX[y(a)]) + " \end{array} \right) \cdot\left( \begin{array}{c} " + (LaTeX[x(b)]) + " \\ " + (LaTeX[y(b)]) + " \end{array} \right) = (" + (LaTeX[x(a)]) + ") \cdot (" + (LaTeX[x(b)]) + ")+ (" + (LaTeX[y(a)]) + ") \cdot (" + (LaTeX[y(b)]) + ") = " + (LaTeX[c]) + ""
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]) + ""
h: (abs(a) * abs(u))
i: abs(a)
j: abs(u)
Text4: "|\vec{a}| \cdot |\vec{b_{\parallel}}| = " + (LaTeX[i]) + " \cdot " + (LaTeX[j]) + " = " + (LaTeX[h]) + ""