$\vec{p}$

$\vec{n}$

$\vec{n}$

$\vec{x}-\vec{p}$

$\vec{x}$

O: (0 | 0 | 0)
p: (2, 0, 4)
n: (0, 1, 2)
u = If(x(n) ≟ 0, (1 | 0 | 0), If[y(n) ≟ 0, (0 | 1 | 0), If[z(n) ≟ 0, (0 | 0 | 1), ((-y(n)) | x(n) | 0)]])
v: n ⊗ u
v0: v / abs(v)
u0: u / abs(u)
P: O + p
Q1: P + (8 * u0) + (8 * v0)
Q3: P - (8 * u0) - (8 * v0)
Q4: P + (8 * u0) - (8 * v0)
Q2: P - (8 * u0) + (8 * v0)
v1, q2, q3, q4, q1 = Polygon(Q2, Q3, Q4, Q1)
a: (u0 * n)
b: (v0 * n)
c: (u0 * v0)
N: P + n
w = Vector(P, N)
Text1: "\vec{p} = \left(\begin{array}{c} " + (LaTeX[x(p)]) + " \\ " + (LaTeX[y(p)]) + " \\ " + (LaTeX[z(p)]) + "
 \end{array}\right)"
Text2: "\vec{n} = \left(\begin{array}{c} " + (LaTeX[x(n)]) + " \\ " + (LaTeX[y(n)]) + " \\ " + (LaTeX[z(n)]) + " \end{array}\right)"
X = (6, -2, 7)
d = Vector(P, X)
e = Vector(O, X)
px = Vector(P, X)
Text4: "\vec{x} =  \left(\begin{array}{c} " + (LaTeX[x(X)]) + " \\ " + (LaTeX[y(X)]) + " \\ " + (LaTeX[z(X)]) + " \end{array}\right)"
f: (px * n)
Text3: "\overrightarrow{PX} = \vec{x} - \vec{p} = \left(\begin{array}{c} " + (LaTeX[x(px)]) + " \\ " + (LaTeX[y(px)]) + " \\ " + (LaTeX[z(px)]) + " \end{array}\right)"
α = Angle(N, P, X)
Text5: "(\vec{x}-\vec{p}) \cdot \vec{n} = \left(\begin{array}{c} " + (LaTeX[x(px)]) + " \\ " + (LaTeX[y(px)]) + " \\ " + (LaTeX[z(px)]) + " \end{array}\right) \cdot \left(\begin{array}{c} " + (LaTeX[x(n)]) + " \\ " + (LaTeX[y(n)]) + " \\ " + (LaTeX[z(n)]) + " \end{array}\right) = " + (LaTeX[f]) + ""