Aerospace Engineering (Satellite Orbit Path Modeling)

A communication satellite is deployed into a geostationary transfer path. Relative to a global earth tracking coordinate center (measured in kilometers), the satellite passes directly through an initial orbital insertion checkpoint at $A = (4200, 1500, 6300)$ and is tracked moving along a linear vector trajectory toward a target deep-space relay node located at $B = (4350, 1620, 6500)$.

1. Write the vector equation $\vec{r}(t)$ that maps out the satellite's linear flight trajectory.
2. Express this trajectory as a set of parametric equations ($x(t), y(t), z(t)$).
3. Determine the satellite's exact 3D spatial coordinates at $t = 0.4$ (representing $40\%$ completion of this flight leg).