$\vec{x}$

$\vec{p}$

$\vec{n}$

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

$\vec{u}$

$\vec{x}$

t = -2 (slider from -5 to 5)
S: (4, 0, 3)
u: (-1, 2, 1)
Q: S + u
N: (4, 3, 4)
P: (4, 2, 2)
A: (0, 0, 2)
p = Vector((0, 0, 0), P)
n = Vector(P, N)
C: (4, 4, 0)
v = Vector(P, N)
X: Q + (t * u)
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)
g = Line(S, Q)
a: (w * n)
Text1: "g: \vec{x} = \underbrace{\left(\begin{array}{c} " + (LaTeX[x(Q)]) + " \\ " + (LaTeX[y(Q)]) + " \\ " + (LaTeX[z(Q)]) + " \end{array}\right)}_{\vec{q}} +\underbrace{" + (LaTeX[t]) + "}_{t} \cdot \underbrace{\left(\begin{array}{c} " + (LaTeX[x(u)]) + " \\ " + (LaTeX[y(u)]) + " \\ " + (LaTeX[z(u)]) + " \end{array}\right)}_{\vec{u
}} =\left(\begin{array}{c} " + (LaTeX[x(X)]) + " \\ " + (LaTeX[y(X)]) + " \\ " + (LaTeX[z(X)]) + " \end{array}\right)"
H: Q + u
b = Vector(Q, H)
c = Vector((0, 0, 0), X)
d: (0 * (2 - t)) + (1 * (2 + (2 * t))) + (2 * (4 + t))
Text3: "E:  \underbrace{\Biggl[ \underbrace{\left(\begin{array}{c} " + (LaTeX[x(Q)]) + " \\ " + (LaTeX[y(Q)]) + " \\ " + (LaTeX[z(Q)]) + " \end{array}\right) + \underbrace{t}_{" + (LaTeX[t]) + "} \cdot \left(\begin{array}{c} " + (LaTeX[x(u)]) + " \\ " + (LaTeX[y(u)]) + " \\ " + (LaTeX[z(u)]) + " \end{array}\right)}_{\vec{x}} - \underbrace{\left(\begin{array}{c} " + (LaTeX[x(p)]) + " \\ " + (LaTeX[y(p)]) + " \\ " + (LaTeX[z(p)]) + " \end{array}\right)}_{\vec{p}}  \Biggl]  \cdot \underbrace{\left(\begin{array}{c} " + (LaTeX[x(n)]) + " \\ " + (LaTeX[y(n)]) + " \\ " + (LaTeX[z(n)]) + " \end{array}\right)}_{\vec{n}}}_{ " + (LaTeX[a]) + "}\overset{?}{=}0"