Vector $(5,0)$ a line on the $x$ axis or is it a point I'm taking a linear algebra course and we have just began learning about vectors. 
Is the vector $(5,0)$ just a line on the $x$ axis or is it a point? In addition, does it have a direction or magnitude? I believe for direction it would be positive but I do not see the magnitude.
 A: One of the goals of a first course in linear algebra is to abstract the geometric notions of objects you have become familiar with to purer mathematical objects. This means that interpreting the underlying meaning of a particular structure is, well, open-ended. This is especially true when one object can take on multiple interpretations in different contexts.
So, if you are working with vectors as directed line segments (as you might in a physics application), then $(5,0)$ might be interpreted as a rightward-pointing vector of magnitude $5$ on the $xy$-plane, under the usual coordinate system.
If you're interested in image processing or computer graphics, then perhaps $(5,0)$ represents a coordinate on an image, which you might think of as a simple point.
Formally, $(5,0)$ is an element of $\mathbb{R}^2$, which simply means that $(5,0)$ is a pair of real numbers (where order matters; that is, $(5,0)\ne (0,5)$). $\mathbb{R}^2$ is a vector space, which is a way of saying that it is a set of pairs $(x,y)$ obeying certain properties of addition and scaling. Abstractly, vectors are simply elements of vector spaces.
The interpretation determines whether geometric notions such as direction or magnitude should be considered. If, for example, $(5,0)$ is the solution to a system of linear equations, such as 
\begin{align}
x+2y&=5 \\
2x+y&=10,
\end{align}
then magnitude might not be a sensible concept to attribute to it.
A: $u = (5,0) \in \mathbb{R}^2$ can be interpreted as coordinates of the arrow from the origin $0=(0,0)$ to point $P =(5,0)$.
Its magnitude is $\lVert u \rVert = \sqrt{5^2 + 0^2} = 5$ using the euclidean norm. 
Its direction is $u/\lVert u \rVert = (5,0)/5 = (1,0)$.
Note however that $u$ might be interpreted as something else, e.g. the function $f(x) = 5 = 5\cdot 1 + 0\cdot x$ and one could still say it has lenght $5$ and direction $g(x) = 1$.
Example of modeling a line:
The endpoints of the vectors $u(t) = t n + u_0$ are on a line through the end point of $u_0$, where $t$ is some real number and $n$ some vector which is representing the direction and $u_0$ is a vector.
One can assign $v = \vec{PQ}$ the vector from point $P$ to point $Q$, this structure is called an affine space.
