\vec{u}

\vec{v}

\vec{u}

\vec{v}

C = (8, 2)
D = (14, 3)
u = Vector(C, D)
A = (7, 4)
O = Intersect(xAxis, yAxis)
G = Translate(O, u)
B = (9, 7)
v = Vector(A, B)
F = Translate(O, v)
α = Angle(G, O, F)
w = Vector(O, F)
z = Vector(O, G)
a = 0 (slider from 0 to 4, step 0.01)
aa = If(a  <  1, a, 1)
E: C + (aa * (A - C))
H: E + u
b = Vector(E, H)
c = OrthogonalLine(H, v)
d = Line(A, B)
I = Intersect(c, d)
bb = If(a  <  1, 0, If[a  <  2, a - 1, 1])
J: H + (bb * (I - H))
e = Segment(H, J)
cc = If(a  <  2, 0, If[a  <  3, a - 2, 1])
K = If((v * u) > 0, Rotate[I, ((cc * 90))°, A], Rotate[I, 360° - ((cc * 90))°, A])
f = If((v * u) > 0, CircleArc[A, I, K], CircleArc[A, K, I])
g = Segment(K, A)
h = OrthogonalLine(K, g)
i = OrthogonalLine(B, h)
L = Intersect(h, i)
dd = If(a  <  3, 0, If[a  <  4, a - 3, 1])
M: K + (dd * (L - K))
j = OrthogonalLine(M, h)
N = Intersect(j, d)
P, k, m, n, a_1 = Polygon(K, M, N, A)
T2: "\vec{u}·\vec{v}=|\vec{u}| \; |\vec{v}| \;  cos α = " + (LaTeX[Length[u]]) + " · " + (LaTeX[Length[v]]) + " · " + (LaTeX[cos(α)]) + " = " + (LaTeX[(v * u)]) + ""
T3: "\vec{u}·\vec{v}=u_{1} \; v_{1}+u_{2} \; v_{2} = " + (LaTeX[x(G)]) + " · " + (LaTeX[x(F)]) + " + " + (LaTeX[y(G)]) + " · " + (LaTeX[y(F)]) + "  = " + (LaTeX[(v * u)]) + ""
T1: "\vec{u}·\vec{v} = " + (LaTeX[(v * u)]) + ""
ux: x(u)
uy: y(u)
vx: x(v)
vy: y(v)
texto1: "\vec{u}=(" + (LaTeX[ux]) + "," + (LaTeX[uy]) + ")"
texto2: "\vec{v}=(" + (LaTeX[vx]) + "," + (LaTeX[vy]) + ")"
texto3: "\alpha=" + (LaTeX[α]) + ""
modu: (ux^(2) + uy^(2))^(1 / 2)
texto4 = SurdText(modu)
modv: (vx^(2) + vy^(2))^(1 / 2)
texto6 = SurdText(modv)
cosa: cos(α)
texto8 = SurdText(cosa)
Q = Midpoint(C, D)
R = Midpoint(A, B)
texto7: "\left| \vec{v} \right| =\sqrt{" + (LaTeX[vx]) + "^2+" + (LaTeX[vy]) + "^2}=" + (LaTeX[texto6]) + "≈" + (LaTeX[modv]) + ""
texto5: "\left| \vec{u} \right| =\sqrt{" + (LaTeX[ux]) + "^2+" + (LaTeX[uy]) + "^2}=" + (LaTeX[texto4]) + "≈" + (LaTeX[modu]) + ""
texto9: "cos \; \alpha≈" + (LaTeX[cosa]) + ""