I am trying to write a simple explanation of the point-direction form of a line.
$\mathbf{l} = \mathbf{a}+t\mathbf{v}$
but using an actual point instead of a vector seems like a more natural way of thinking about it.
$\mathbf{l} = P+t\mathbf{v}$
but I also want to do the coordinate form of a line, which would look like:
$x=P_1+tv_1$
$y=P_2+tv_2$
$z=P_3+tv_3$
and now I'm in this silly situation of worrying about if I can write it out in the way that makes the most sense without being wrong. So can I do it like that or do I have to do it as a vector?