Parabola from vector equation. 3 dimensions.
Once a reference plane is chosen, the formula is identical to the one in
Worksheet 1: http://www.geogebratube.org/material/show/id/32226
O, the magic of vectors.

Notes:
3-dimensional rotation cannot in general be treated as algebraic. Reference axes can be updated continuously as, for example,
SetValue[Δτ, τ - τPrev]
SetValue[e, e cos(Δτ) + g sin(Δτ)]
SetValue[τPrev, τ]
(and a periodic normalization)
for the angle of rotation, for free point F.
In 3-space the cross product is a vector product.
Random things for Slumberland to remember:
How an object moves in space is given by the motion itself. For real-time application I adopt the following assumptions:
1) Time and space are continuous.
2) If the system to be integrated is coupled kinematics and dynamics, and it is integrated linearly in time,
it can be made stable.
Respect the nonlinear differential system.
Set-theoretical obstacles to adopting these assumptions are pretend and I will ignore them.