A line is essentially a vector (which determines the direction) that is of infinite length, which is then positioned somewhere.

So basically, what has happened to get the line is that determines the direction of the line, it is multiplied by some parameter to make it of infinite length, and then the point has been added (or rather, each component of is adjusted numerically by each component of ) to position it in the correct spot.

Do you think you can get a vector-form equation for the line passing through B in the direction of ?