Calculus 3: Equations of lines and planes

Given a fixed point $P_0$ with coordinates $(x_0, y_0, z_0)$ and a direction vector $\vec{v}$ in three-dimensional space, find the vector equation of a line that passes through $P_0$ and is parallel to $\vec{v}$.

Find a vector equation and parametric equations for the line that passes through the point $(5, 1, 3)$ and is parallel to the vector $\mathbf{v} = (1, 4, -2)$. Then find two other points on the line.