$\vec{a}$

$\vec{v}$

$\vec{w}$

$\vec{x}$

$r \cdot \vec{v} + s \cdot \vec{w}$

E: \vec{x} = \vec{q} + r \cdot \vec{v} + s \cdot \vec{w}

O: (0, 0, 0)
E = Surface((0, 1, 4) + (r * (-0.5, 1, 0)) + (s * (-0.5, 0, 0.5)), r, -10, 10, s, -10, 10)
D_{(1,-1)}: E(1, -1)
D_{(-1,0)}: E(-1, 0)
D_{(0,1)}: E(0, 1)
C: E(0, 2)
D_{(0,0)}: E(0, 0)
D_{(1,0)}: E(1, 0)
D_{(1,1)}: E(1, 1)
D_{(0,-1)}: E(0, -1)
D_{(-1, 1)}: E(-1, 1)
D_{(-1,-1)}: E(-1, -1)
D_{(2,0)}: E(2, 0)
D_{(2,1)}: E(2, 1)
D_{(2,-1)}: E(2, -1)
D_{(0,2)}: E(0, 2)
D_{(-1,2)}: E(-1, 2)
D_{(1,2)}: E(1, 2)
D_{(2,2)}: E(2, 2)
D_{(-2,0)}: E(-2, 0)
D_{(-2,1)}: E(-2, 1)
D_{(-2,2)}: E(-2, 2)
D_{(-2,-1)}: E(-2, -1)
D_{(3,0)}: E(3, 0)
D_{(3,1)}: E(3, 1)
D_{(3,2)}: E(3, 2)
D_{(3,-1)}: E(3, -1)
A: E(0, 0)
q = Vector(O, A)
B: E(2, 0)
v = Vector(A, B)
w = Vector(A, C)
r = 0.5 (slider from -5 to 5, step 0.1)
s = 0.2 (slider from -5 to 5, step 0.1)
X: q + (r * v) + (s * w)
a = Vector(O, X)
u = Vector(A, X)
d1, c, a_1, b = Polygon(A, B, C)
Text1: "\vec{x} =  \underbrace{\begin{pmatrix}" + (LaTeX[x(q)]) + "\\" + (LaTeX[y(q)]) + "\\" + (LaTeX[z(q)]) + "\end{pmatrix}}_{\substack{\vec{a}}} +\underbrace{(" + (LaTeX[r]) + ")}_{\substack{r}} \cdot \underbrace{\begin{pmatrix}" + (LaTeX[x(v)]) + "\\" + (LaTeX[y(v)]) + "\\" + (LaTeX[z(v)]) + "\end{pmatrix}}_{\substack{\vec{v}}} +\underbrace{(" + (LaTeX[s]) + ")}_{\substack{s}}\cdot \underbrace{\begin{pmatrix}" + (LaTeX[x(w)]) + "\\" + (LaTeX[y(w)]) + "\\" + (LaTeX[z(w)]) + "\end{pmatrix}}_{\substack{\vec{w}}} = \begin{pmatrix}" + (LaTeX[x(X)]) + "\\" + (LaTeX[y(X)]) + "\\" + (LaTeX[z(X)]) + "\end{pmatrix}"