TITLE: How can a vector represent velocity and a position as well?
QUESTION [5 upvotes]: I'm relatively new to linear algebra. I've got a question about a question. I'm not looking for the exact answer (I'll try to find it by myself).
I stumbled upon the following question :
"*At 12:00 pm, a spaceship is at position $$\begin{pmatrix}
3 \\
2\\
4
\end{pmatrix}$$km away from the origin with respect to some 3 dimensional co ordinate system. The ship is travelling with velocity $$\begin{pmatrix}
-1 \\
2\\
-3
\end{pmatrix}$$km/h What is the location of the spaceship after 2 hours have passed?".
I understand what a 
$$\begin{pmatrix}
3 \\
2\\
4
\end{pmatrix}$$
position means (in three dimensional Cartesian coordinate system with x, y, z axes). 
I can point precisely the position on a paper. But what does a " [-1,2,-3] velocity " mean ?
Again, I'm not looking for the precise answer. I'd just like to know how to approach the problem since a same format (vectors) is used to tackle two different concepts (namely, position and velocity). How can I process to some calculations in this "position" I would say, aha.
Thank you :)
Alex

REPLY [2 votes]: Answer spoiler!
We are already given a 3-dimensional position. From that position, we move to $\begin{pmatrix}-1 \\ 2 \\ -3\end{pmatrix}$ per hour. So, to figure out the position after two hours travelling this velocity, write $\begin{pmatrix}3 \\ 2 \\ 4\end{pmatrix} + 2 * \begin{pmatrix}-1 \\ 2 \\ -3\end{pmatrix}$.