$[c^2, c^3, c^4] \text { parallel to/same direction as } [1,-2,4]$
Find $c$ if it exists.
How do I see if they are parallel and find a c?
Generally, we can say that $r[1,-2,4] = [c^2, c^3, c^4]$
But then I have two unknowns and I don't know how to solve like this?
As $[c^2,c^2,c^4]=c^2[1,c,c^2]$ is parallel to and has the same direction as $[1,c,c^2]$, this amounts to solving the same problem for the latter. Actually, one can obviously find $c$ such that $[1,c,c^2]$ is not only parallel, but equal to $[1,-2,4]$.
Consider $$c=\frac {c^3}{c^2}=\frac {c^4}{c^3}=?$$