$\vec{u}$

$\vec{p}$

$\vec{x}$

$t \cdot \vec{u}$

t = 4 (slider from -10 to 10, step 0.1)
O: (0 | 0 | 0)
P = Point(g)
Q = Point(g)
u = Vector(P, Q)
v = Vector(O, P)
X: P + (t * u)
w = Vector(O, X)
Text2: "g: \vec{x} = \left(\begin{array}{c} " + (LaTeX[x(P)]) + " \\ " + (LaTeX[y(P)]) + " \\ " + (LaTeX[z(P)]) + "\end{array}\right) + t \cdot \left(\begin{array}{c} " + (LaTeX[x(u)]) + " \\ " + (LaTeX[y(u)]) + " \\ " + (LaTeX[z(u)]) + "\end{array}\right)"
a = Vector(P, 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}}"