$\vec{p}$

$\vec{x}$

$\vec{n}$

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

O: (0 | 0 | 0)
N: (4 | 1 | 4)
P: (3 | 1 | 2)
n_{1} = Vector(P, N)
p = Vector((0 | 0 | 0), P)
E: (x(n_{1}) * x) + (y(n_{1}) * y) + (z(n_{1}) * z) = (p * n_{1})
X = PointIn(E)
A: (0 | 0 | 2)
u = Vector(O, X)
b: ((u - p) * n_{1})
C: (4 | 4 | 0)
n = Vector(P, N)
w = Vector(P, X)
α = Angle(X, P, N)
Ebene = 1 (slider from -5 to 5)
a: (p * n_{1})
Text3: " \Biggl[ \underbrace{\left(\begin{array}{c} x_1 \\ x_2 \\ x_3 \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_{1})]) + " \\ " + (LaTeX[y(n_{1})]) + " \\ " + (LaTeX[z(n_{1})]) + " \end{array}\right)}_{\vec{n}} = " + (LaTeX[b]) + ""
Text1: "\underbrace{" + (LaTeX[x(n_{1})]) + "x_1 + " + (LaTeX[y(n_{1})]) + "x_2 + " + (LaTeX[z(n_{1})]) + "x_3}_{\vec{x}\cdot\vec{n}} = \underbrace{" + (LaTeX[a]) + "}_{\vec{p}\cdot\vec{n}}"