\theta

$\displaystyle \frac{\vec u \cdot \vec v}{\|\vec u\| \|\vec v\|}$

1

-1

90°

180°

0

A = Intersect(xAxis, yAxis)
B = (1, 2)
C = (-1, 1)
u = Vector(A, C)
v = Vector(A, B)
a: x(B) * x(C) + y(B) * y(C)
u1: x(C)
u2: y(C)
v1: x(B)
v2: y(B)
texto1: "Produto escalar :
$\vec u \cdot \vec v = (" + (LaTeX[u1]) + ")\times(" + (LaTeX[v1]) + ")+(" + (LaTeX[u2]) + ")\times(" + (LaTeX[v2]) + ") = " + (LaTeX[a]) + "$"
θ = Angle(v, u)
D = (0.54, 3.68)
b = Line(D, xAxis)
E = (3.62, 2.2)
c = Line(E, yAxis)
F = Intersect(b, c)
e = CurveCartesian(x(F) + t, y(F) + cos(t), t, 0, 3.141592653589793)
G = (2.4, 5.78)
H = (2.4, 2.32)
I = (7.76, 2.32)
J = (7.76, 5.78)
polígono1, g, h, i, j = Polygon(G, H, I, J)
d = Segment(G, H)
f = Segment(J, I)
k = Segment(I, H)
l = Segment(G, J)
K = Intersect(b, d)
L = Intersect(b, f)
M = Intersect(c, l)
N = Intersect(c, k)
w = Vector(K, L)
z = Vector(N, M)
O = Point(e)
m = OrthogonalLine(O, w)
P = Intersect(b, m)
n = Segment(O, P)
t = Line(O, b)
T = Intersect(c, t)
a_1 = Segment(T, O)
texto2: "Ângulo entre $\vec u$ e $\vec v$:
$\theta=∡(\vec u, \vec v) =" + (LaTeX[θ]) + ""
nu: sqrt(x(C)^(2) + y(C)^(2))
nv: sqrt(x(B)^(2) + y(B)^(2))
co: a / (nu * nv)
texto6: "$\frac{\vec u \cdot \vec v}{\|\vec u\| \|\vec v\|}=\frac{" + (LaTeX[a]) + "}{" + (LaTeX[nu]) + "\times" + (LaTeX[nv]) + "}=" + (LaTeX[co]) + "$ "
Pc: (x(F) + θ, y(F) + co)
texto7: "" + co + ""
p = Line(Pc, w)
q = Line(Pc, z)
Q = Intersect(c, p)
R = Intersect(b, q)
r = Segment(Q, Pc)
s = Segment(Pc, R)
texto8: "" + θ + ""