Produit scalaire
Author: Daniel Mentrard
Date: 7 novembre 2008

The scalar product can be calculated in two ways. 
Combining these ways gives a method of calculating the angle between two vectors.

 Quelle est la relation entre le produit   scalaire 
 et l'aire de ce rectangle?
 Observez si:  u.v > 0   ;  u.v < 0   ; u.v = 0 ;
 u = v  ;   u = -v  

Modifiez les vecteurs ici

D = (20, 0)
C = (13, 0)
v = Vector(C, D)
s_2: (x(v))^(2) + (y(v))^(2)
B = (18, 4)
A = (13, 0)
u = Vector(A, B)
s_1: (x(u))^(2) + (y(u))^(2)
E = (0, 0)
E' = Translate(E, v)
h = Circle(E, E')
d = Line(E, E')
w = Vector(E, E')
E'_1 = Translate(E, u)
a = OrthogonalLine(E'_1, w)
F = Intersect(a, d)
b = OrthogonalLine(E'_1, a)
c = OrthogonalLine(E, b)
H, I = Intersect(h, c)
i = OrthogonalLine(H, c)
J = Intersect(a, i)
z = Vector(E, E'_1)
θ = Angle(w, z)
prdscal: (x(u) * x(v)) + (y(u) * y(v))
poly1, e, f, g, j = Polygon(J, F, E, H)
poly2, k, l, m, n = Polygon(J, H, E, F)
text3: "u.v  =  " + prdscal
text4: "u.v  =  " + prdscal
text5: "u.v  =  " + prdscal
p = Segment(E'_1, F)
q = Line(E, xAxis)
G, K = Intersect(h, q)
r = Segment(E, K)
L = (15, 9)
M = (-10, 10)
N = (10, 10)
O = (10, -10)
P = (-10, -10)
poly3, m_1, n_1, o, p_1 = Polygon(M, N, O, P)
Textepoly1: "Aire du rectangle donnée par Geogebra : " + poly1
Q = (14, 10)
R = (18, 10)
S = (18, 9)
T = (14, 9)
poly4, q_1, r_1, s, t = Polygon(Q, R, S, T)