Two vectors are parallel if they are multiples of each other
ie \vec{a}= <1,2,3> is parallel to \vec{b}=<2,4,6> and \vec{c}=<3,6,9> and so on
So the parameter t in \vec{a} = \vec{v}t just allows the vector \vec{r} to move along the line, where \vec{r} is the position vector of a point on...