Equations of lines and planes Hi guys I just have a few technicality and terminology questions about equations of lines and planes.
Just say we have a line represented by the vector equation:
r = r0 + tv, where t is an element of real numbers and r0, r, v are vectors.

I kindly request to know if it is correct to say that r is the line or treat r as a function of t. I read around but I just want a second opinion. I know r is a position vector but can I also say that it is the line as well?
What  do the symmetric equations of the line tell me. I mean just say I have two lines and they are parallel, will the symmetric equations show me any evidence if this?

The line is not $r$ ( note that $r$ is  really vector $\vec r$, that I suppose in $\mathbb{R}^3$) but the graph of the function 
$$
f=\mathbb{R} \to \mathbb{R}^3
$$
defined as:
$$
\vec r= f(t)=\begin{pmatrix}x\\y\\z\end{pmatrix}=\begin{pmatrix}x_0\\y_0\\z_0\end{pmatrix}+t\begin{pmatrix}x_v\\y_v\\z_v\end{pmatrix}=\vec r_0+t\vec v
$$ 
so we can say , with a little abuse, that $\vec r$ is a point of the line.
