$\vec{v}$

p: (2, -2, 2)
u: (-0.5, 1, 0.5)
g = Line((x(p), y(p), z(p)), Vector[(x(u), y(u), z(u))])
D_{1} = (1.5, -1, 2.5)
P = (3, -4, 1)
D: (-0.5, 3, 4.5)
v = Vector(P, D_{1})