 \Biggl(

$\vec{p}$

$\vec{x}$

X

\Biggr)

|

|

$\vec{n}$

$\overrightarrow{PX}$

$\vec{n_0}$

$\overrightarrow{PX}_{\parallel}$

$\overrightarrow{PX}_{\perp}$

N: (1 | 1 | 0)
P: (1 | -3 | 3)
A: (0 | 0 | 2)
x1 = 3 (slider from -5 to 5, step 0.5)
x2 = 1 (slider from -5 to 5, step 0.5)
x3 = 3 (slider from -5 to 5, step 0.5)
p = Vector((0 | 0 | 0), P)
n = Vector(P, N)
u: (x1, x2, x3)
b: ((u - p) * n)
X: (x1 | x2 | x3)
C: (4 | 4 | 0)
v = Vector(P, N)
w = Vector(P, X)
α = Angle(X, P, N)
Ebene = 1 (slider from -5 to 5)
r: (x(n) * x) + (y(n) * y) + (z(n) * z) = (p * n)
a_{1} = Vector(P, X)
f = OrthogonalLine(X, r)
F = Intersect(f, r)
d = Segment(F, X)
n0: n / abs(n)
N0: P + n0
c = Vector(P, N0)
h = Line(N0, P)
i = OrthogonalLine(X, h, space)
B = Intersect(i, h)
D = Intersect(h, i)
d_{1} = Vector(P, B)
e = Vector(B, X)
g: (w * n0)
Text3: "d:  \underbrace{\left(\begin{array}{c} " + (LaTeX[x(w)]) + " \\ " + (LaTeX[y(w)]) + " \\ " + (LaTeX[z(w)]) + " \end{array}\right)}_{\overrightarrow{PX}}  \cdot \underbrace{\left(\begin{array}{c} " + (LaTeX[x(n0)]) + " \\ " + (LaTeX[y(n0)]) + " \\ " + (LaTeX[z(n0)]) + " \end{array}\right)}_{\vec{n_0}} = " + (LaTeX[g]) + ""
Text2: "E:  \underbrace{\left[\vec{x} - \left(\begin{array}{c} " + (LaTeX[x(P)]) + " \\ " + (LaTeX[y(P)]) + " \\ " + (LaTeX[z(P)]) + " \end{array}\right)\right]}_{\overrightarrow{PX}}  \cdot \underbrace{\left(\begin{array}{c} " + (LaTeX[x(n)]) + " \\ " + (LaTeX[y(n)]) + " \\ " + (LaTeX[z(n)]) + " \end{array}\right)}_{\vec{n}} = 0"