Vector parametrization of the line that passes through two vectors. How would I find the vector parametrization  $()$  of the line  $L$  that passes through the points  $(2,1,4)$  and  $(5,6,7)$?
So I found a directional vector: $(3,5,3)$.
What do I do next?

You found a direction vector $(3,5,3)=(5,6,7)-(2,1,4)$,
so the line can be parametrized as $(2,1,4)+t(3,5,3)=(2+3t,1+5t,4+3t)$.
Note that $\mathbf r(0)=(2,1,4)$ and $\mathbf r(1)=(5,6,7)$.
