$\vec{u}$

$\vec{p}$

$\vec{x}$

g: \vec{x} = \vec{p} + t \cdot \vec{u}

$t \cdot \vec{u}$

$\vec{u}$

u: (-1, 1, 0.5)
O: (0, 0, 0)
P: (1, -2, 2)
p = Vector(O, P)
Q: p + u
g = Line((x(p), y(p), z(p)), Vector[(x(u), y(u), z(u))])
t = 4 (slider from -10 to 10, step 0.1)
X: p + (t * u)
w = Vector(O, X)
a = Vector(P, X)
b = Vector(P, Q)
Text1: "\vec{x} = \vec{p} + t \cdot \vec{u} = \begin{pmatrix}" + (LaTeX[x(P)]) + "\\" + (LaTeX[y(P)]) + "\\" + (LaTeX[z(P)]) + "\end{pmatrix} + (" + (LaTeX[t]) + ") \cdot \begin{pmatrix}" + (LaTeX[x(u)]) + "\\" + (LaTeX[y(u)]) + "\\" + (LaTeX[z(u)]) + "\end{pmatrix} = \begin{pmatrix}" + (LaTeX[x(X)]) + "\\" + (LaTeX[y(X)]) + "\\" + (LaTeX[z(X)]) + "\end{pmatrix}"