Shortest distance between a point and a line - Vectors

I'd just like it if someone could tell me where it is I'm going wrong in my calculations.. It might even be at the very beginning, I'm at a loss. ):

'Find the distance from the point P(3,0,-1) to the line with equation '

Any point on the line I got to be .

That means that , and the direction vector of the line is

Then I tried to calculate their scalar product to find when they are perpendicular and thus closest to each other, but then I got to be 0...

So would someone please tell me where it is I go wrong?

Is it something at the very beginning? ):

And then another question that is very simple!

What is the direction vector of the line 3x-y=4?

A fixed point would be (0,-4), right?

Thanks in advance!