Q:

How to find line parallel to direction vector and passing through a specific point?

I am give the point $(1,0,-3)$ and the vector $2i-4j+5k$
Find the equation of the line parallel to vector and passing through point $(1,0,-3)$
Could one use the fact that the dot product between the line and the vector?
Please give me some direction as where to go for this question. I am so lost

A:

In general, we know that the equation of the line passing through the point $(x_1, y_1, z_1)$ & parallel to the vector $(ai+bj+ck)$ is given as $$\frac{x-x_1}{a}=\frac{y-y_1}{b}=\frac{z-z_1}{c}$$ 
Hence, the equation of the line passing through the point $(1, 0, -3)$ & parallel to the vector $(2i-4j+5k)$ is given as $$\frac{x-1}{2}=\frac{y-0}{-4}=\frac{z-(-3)}{5}$$ 
$$\frac{x-1}{2}=\frac{-y}{4}=\frac{z+3}{5}$$ It can also be represented as 

$$r(t)=(1, 0, -3)+t(2, -4, 5)$$

