Answer
$ P $ does not lie on the path
$ Q $ lies on the path
Work Step by Step
For the point $ P=(4,11,20)$, we have the system
$$1+t=4, \quad 2+t^2=11, \quad t^4=20$$
which has no solutions since the first equation gives $ t=3$ which is not a solution for the third equation. Hence, $ P $ does not lie on the given path.
For the point $ Q=(-1,6,16)$, we have the system
$$1+t=-1, \quad 2+t^2=6, \quad t^4=16$$
which has the solution $ t=2$. Hence, $ Q $ lies on the given path.
