$\vec{u}$

$\vec{p}$

$\vec{x}$

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

t = 0 (slider from 0 to 10, step 0.1)
O: (0, 0, 0)
P: (3, -1, 2)
Q: (2, -0.5, 2.5)
u = Vector(P, Q)
v = Vector(O, P)
X: g(t)
w = Vector(O, X)
Text1: "\orange{\vec{x}} = \blue{\vec{p}} + t \cdot \violet{\vec{u}} = \blue{\begin{pmatrix}" + (LaTeX[x(P)]) + "\\" + (LaTeX[y(P)]) + "\\" + (LaTeX[z(P)]) + "\end{pmatrix}} + " + (LaTeX[t]) + " \cdot \violet{\begin{pmatrix}" + (LaTeX[x(u)]) + "\\" + (LaTeX[y(u)]) + "\\" + (LaTeX[z(u)]) + "\end{pmatrix}} = \orange{\begin{pmatrix}" + (LaTeX[x(X)]) + "\\" + (LaTeX[y(X)]) + "\\" + (LaTeX[z(X)]) + "\end{pmatrix}}"