a_1

a_2

a_3

a_4

a=(a_1,a_2,a_3,a_4) ist der Vektor, 
in dessen Richtung projiziert 
wird, auf eine Hyperebene 
= 3DRaum, der senkrecht 
auf a steht.

b1 = 1.7 (slider from -5 to 5, step 0.1)
b2 = 1 (slider from -5 to 5, step 0.1)
b3 = 0.8 (slider from -5 to 5, step 0.1)
b4 = 1.5 (slider from -5 to 5, step 0.1)
l: sqrt(b1^(2) + b2^(2) + b3^(2) + b4^(2))
a1: b1 / l
a2: b2 / l
a3: b3 / l
a4: b4 / l
A: (((-a2)) / (a1^(2) + a2^(2)), 0, a1 / (a1^(2) + a2^(2)))
B: (a1 / (a1^(2) + a2^(2)), 0, a2 / (a1^(2) + a2^(2)))
C: (0, ((-a4)) / (a3^(2) + a4^(2)), ((-a3)) / (a3^(2) + a4^(2)))
D: (0, a3 / (a3^(2) + a4^(2)), ((-a4)) / (a3^(2) + a4^(2)))
O = Intersect(yAxis, zAxis)
u = Vector(O, A)
v = Vector(O, B)
w = Vector(O, C)
a = Vector(O, D)
E: B + u
F: A + w
G: B + w
H: E + w
f = Segment(B, E)
g = Segment(E, A)
h = Segment(A, O)
i = Segment(O, B)
j = Segment(C, F)
k = Segment(F, H)
m = Segment(H, G)
n = Segment(G, C)
p = Segment(E, H)
q = Segment(B, G)
r = Segment(A, F)
s = Segment(O, C)
I: A + a
J: B + a
K: C + a
M: E + a
N: F + a
P: G + a
Q: H + a
t = Segment(M, Q)
b = Segment(Q, P)
c = Segment(P, J)
d = Segment(J, M)
e = Segment(I, N)
f_1 = Segment(N, K)
g_1 = Segment(K, D)
h_1 = Segment(D, I)
i_1 = Segment(Q, N)
j_1 = Segment(M, I)
k_1 = Segment(P, K)
l_1 = Segment(J, D)
m_1 = Segment(F, N)
n_1 = Segment(A, I)
p_1 = Segment(C, K)
q_1 = Segment(O, D)
r_1 = Segment(H, Q)
s_1 = Segment(E, M)
t_1 = Segment(G, P)
a_1 = Segment(B, J)
u_1 = Vector(G, F)
v_1 = Vector(G, A)
w_1 = Vector(G, I)
α = Angle(I, G, A)
β = Angle(I, G, F)
L = (-2.972, 3.976)
R = (-1.272, 3.976)